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cosolver/FM/FMsamples/RK14FM.f95
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RK14FM.f95
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SUBROUTINE FM_RK14( A, B, N_ORDER, FM_RK14_F, N_FUNCTION, S, TOL, S1 )
! Solve the vector first-order differential equation s' = f(x,s).
! This routine uses 14th order Runge-Kutta with adjustable step size, starting at x = A
! with state vector S (initial conditions), and returns state vector S1 as the solution
! at x = B.
! N_ORDER is the order of the differential equation (length of vectors S and S1).
! N_FUNCTION is the function number (used in FM_RK14_F) identifying which function f(x,s)
! defines the right-hand-side of the differential equation to be solved.
! TOL is the absolute error tolerance. Because the coefficients are defined with no more than
! about 85-digit precision, TOL should not be less than 1.0e-75.
! The FM precision level should be set to at least 10 digits more than TOL.
! For example, set precision with CALL FM_SET(30) if FM_RK14 will be called with TOL = 1.0e-20.
! The error estimate that is used to control step size will fail if f(x,s) is a function of
! x only, not depending on s. In this case, the differential equation is really just an
! integration problem and should be done as a numerical integration.
USE FMZM
IMPLICIT NONE
INTEGER, PARAMETER :: MAXIMUM_ORDER = 3
INTEGER :: J, N_ORDER, N_FUNCTION
TYPE (FM) :: A, B, TOL, S(MAXIMUM_ORDER), S1(MAXIMUM_ORDER)
TYPE (FM), SAVE :: ERROR_EST, H, TOL2, X
EXTERNAL :: FM_RK14_F
LOGICAL, SAVE :: LAST_STEP
CALL FM_ENTER_USER_ROUTINE
IF (TOL < TO_FM(' 1.0e-75 ')) THEN
WRITE (*,*) ' '
WRITE (*,*) ' Error in input to FM_RK14. TOL should not be less than 1.0e-75. It was'
CALL FM_PRINT(TOL)
WRITE (*,*) ' '
STOP
ENDIF
! Pick an initial step size.
TOL2 = ABS(TOL) / 1000
H = ABS(TOL2)**(1.0D0/14)
X = A
LAST_STEP = .FALSE.
DO J = 1, 10**7
IF (X+H >= B) THEN
H = B - X
LAST_STEP = .TRUE.
ENDIF
CALL FM_RK14_STEP( N_ORDER, FM_RK14_F, N_FUNCTION, X, S, H, ERROR_EST, S1 )
! If the error is too big, try again with halved step size.
IF (ERROR_EST > TOL2) THEN
H = H / 2
CYCLE
ENDIF
! Make the step.
IF (LAST_STEP) THEN
EXIT
ENDIF
S(1:N_ORDER) = S1(1:N_ORDER)
X = X + H
! If the error is much smaller than TOL2, try doubling the step size.
! Otherwise, if the error is less than TOL2/10, try to fine-tune the
! step size by increasing H slightly.
IF (ERROR_EST < TOL2/1.0D+5) THEN
H = 2*H
ELSE IF (ERROR_EST < TOL2/10) THEN
H = 1.05*H
ENDIF
ENDDO
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_RK14
SUBROUTINE FM_RK14_STEP( N_ORDER, FM_RK14_F, N_FUNCTION, X, S, H, ERROR_EST, S1 )
! Do one step of 14th order Runge-Kutta, starting with state vector S(X) and returning
! state vector S1(X+H) after a step of H.
! N_ORDER is the order of the differential equation (length of vector S).
! N_FUNCTION is the function number (used in FM_RK14_F) identifying which function is to be solved.
USE FMVALS
USE FMZM
IMPLICIT NONE
INTEGER, PARAMETER :: MAXIMUM_ORDER = 3
INTEGER :: J, K, N_STAGES, N_ORDER, N_FUNCTION
TYPE (FM) :: H, ERROR_EST, S(MAXIMUM_ORDER), S1(MAXIMUM_ORDER), X
TYPE (FM), SAVE :: A(0:34), B(0:34,0:34), C(0:34), FI_J(MAXIMUM_ORDER,0:34), &
FI(MAXIMUM_ORDER), YK(0:34,MAXIMUM_ORDER), Y(MAXIMUM_ORDER)
EXTERNAL :: FM_RK14_F
INTEGER, SAVE :: COEFF_BASE = 0, COEFF_PRECISION = 0
CALL FM_ENTER_USER_ROUTINE
N_STAGES = 35
IF (COEFF_BASE /= MBASE .OR. COEFF_PRECISION < NDIG) THEN
COEFF_BASE = MBASE
COEFF_PRECISION = NDIG
CALL FM_RK14_COEFFS(A, B, C)
ENDIF
! Do the step.
YK(0,1:N_ORDER) = S(1:N_ORDER)
DO K = 1, N_STAGES - 1
YK(K,1:N_ORDER) = 0
DO J = 0, K-1
IF (J == K-1) THEN
Y(1:N_ORDER) = YK(J,1:N_ORDER)
CALL FM_RK14_F(N_ORDER, N_FUNCTION, X+A(J)*H, Y, FI)
FI_J(1:N_ORDER,J) = FI(1:N_ORDER)
ENDIF
IF (B(K,J) /= 0) THEN
YK(K,1:N_ORDER) = YK(K,1:N_ORDER) + B(K,J) * FI_J(1:N_ORDER,J)
ENDIF
ENDDO
YK(K,1:N_ORDER) = YK(0,1:N_ORDER) + H * YK(K,1:N_ORDER)
ENDDO
S1(1:N_ORDER) = 0
DO K = 0, N_STAGES - 1
IF (K == N_STAGES-1) THEN
Y(1:N_ORDER) = YK(K,1:N_ORDER)
CALL FM_RK14_F(N_ORDER, N_FUNCTION, X+A(K)*H, Y, FI)
S1(1:N_ORDER) = S1(1:N_ORDER) + C(K) * FI(1:N_ORDER)
ELSE
S1(1:N_ORDER) = S1(1:N_ORDER) + C(K) * FI_J(1:N_ORDER,K)
ENDIF
ENDDO
S1(1:N_ORDER) = S(1:N_ORDER) + H * S1(1:N_ORDER)
ERROR_EST = H * ( NORM2( FI_J(1:N_ORDER,33) - FI_J(1:N_ORDER,1) ) ) / 1000
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_RK14_STEP
SUBROUTINE FM_RK14_COEFFS(A, B, C)
! Define the coefficients used in the RK14 formula (85 digits).
! These came from:
! http://www.peterstone.name/Maplepgs/Maple/nmthds/RKcoeff/Runge_Kutta_schemes/RK14/RKcoeff14a_1.pdf
USE FMZM
IMPLICIT NONE
TYPE (FM) :: A(0:34), B(0:34,0:34), C(0:34)
CALL FM_ENTER_USER_ROUTINE
! Many of the coefficients are zero. Initialize A, B, and C here, then
! skip those definitions below.
A = 0
B = 0
C = 0
A( 1) = TO_FM(' 1 ') / 9
A( 2) = TO_FM(' 5 ') / 9
A( 3) = TO_FM(' 5 ') / 6
A( 4) = TO_FM(' 1 ') / 3
A( 5) = TO_FM(' 1 ')
A( 6) = TO_FM(' .6699869792727729217646837855059985139388452296384603532851421391683474428303956826239 ')
A( 7) = TO_FM(' .2970683842138183573895847168082194132233320946989156873791682903324708698499266217383 ')
A( 8) = TO_FM(' 8 ') / 11
A( 9) = TO_FM(' .1401527990421887652761874879669467176298064630825329362873230163439023340348096838456 ')
A(10) = TO_FM(' .7007010397701507371510998548307493379414070492655464089692218490447945746638665522966 ')
A(11) = TO_FM(' 4 ') / 11
A(12) = TO_FM(' 5 ') / 19
A(13) = TO_FM(' .392172246650270859125196642501208648863714315266128052078483e-1 ')
A(14) = TO_FM(' .8129175029283767629833931592780365061896123726172385507744269795906758195776958783707 ')
A(15) = TO_FM(' 1 ') / 6
A(16) = TO_FM(' 9 ') / 10
A(17) = TO_FM(' .6412992574519669233127711938966828094810966516150832254029235721305050295351572963693e-1 ')
A(18) = TO_FM(' .2041499092834288489277446343010234050271495052413337516288702042649259099754335560687 ')
A(19) = TO_FM(' .3953503910487605656156713698273243723522272974566594505545766538389345381768585023057 ')
A(20) = TO_FM(' .6046496089512394343843286301726756276477727025433405494454233461610654618231414976943 ')
A(21) = TO_FM(' .7958500907165711510722553656989765949728504947586662483711297957350740900245664439313 ')
A(22) = TO_FM(' .9358700742548033076687228806103317190518903348384916774597076427869494970464842703631 ')
A(23) = TO_FM(' 1 ') / 6
A(24) = TO_FM(' .8129175029283767629833931592780365061896123726172385507744269795906758195776958783707 ')
A(25) = TO_FM(' .392172246650270859125196642501208648863714315266128052078483e-1 ')
A(26) = TO_FM(' 4 ') / 11
A(27) = TO_FM(' .7007010397701507371510998548307493379414070492655464089692218490447945746638665522966 ')
A(28) = TO_FM(' .1401527990421887652761874879669467176298064630825329362873230163439023340348096838456 ')
A(29) = TO_FM(' .2970683842138183573895847168082194132233320946989156873791682903324708698499266217383 ')
A(30) = TO_FM(' .6699869792727729217646837855059985139388452296384603532851421391683474428303956826239 ')
A(31) = TO_FM(' 1 ') / 3
A(32) = TO_FM(' 5 ') / 9
A(33) = TO_FM(' 1 ') / 9
A(34) = TO_FM(' 1 ')
C( 0) = TO_FM(' 1 ') / 56
C( 1) = TO_FM(' 3 ') / 512
C( 2) = TO_FM(' 3 ') / 256
C( 4) = TO_FM(' 9 ') / 512
C( 6) = TO_FM(' 3 ') / 128
C( 7) = TO_FM(' 15 ') / 512
C( 9) = TO_FM(' 9 ') / 256
C(10) = TO_FM(' 21 ') / 512
C(11) = TO_FM(' 3 ') / 64
C(13) = TO_FM(' 27 ') / 512
C(14) = TO_FM(' 15 ') / 256
C(15) = TO_FM(' 33 ') / 512
C(17) = TO_FM(' .1053521135717530196914960328878781622276730830805238840416702908213176249782427570033 ')
C(18) = TO_FM(' .1705613462417521823821203385538740858875554878027908047375010369442754416180982144816 ')
C(19) = TO_FM(' .2062293973293519407835264857011048947419142862595424540779715293772640762608018856579 ')
C(20) = TO_FM(' .2062293973293519407835264857011048947419142862595424540779715293772640762608018856579 ')
C(21) = TO_FM(' .1705613462417521823821203385538740858875554878027908047375010369442754416180982144816 ')
C(22) = TO_FM(' .1053521135717530196914960328878781622276730830805238840416702908213176249782427570033 ')
C(23) = TO_FM(' -33 ') / 512
C(24) = TO_FM(' -15 ') / 256
C(25) = TO_FM(' -27 ') / 512
C(26) = TO_FM(' -3 ') / 64
C(27) = TO_FM(' -21 ') / 512
C(28) = TO_FM(' -9 ') / 256
C(29) = TO_FM(' -15 ') / 512
C(30) = TO_FM(' -3 ') / 128
C(31) = TO_FM(' -9 ') / 512
C(32) = TO_FM(' -3 ') / 256
C(33) = TO_FM(' -3 ') / 512
C(34) = TO_FM(' 1 ') / 56
B( 1, 0) = TO_FM(' 1 ') / 9
B( 2, 0) = TO_FM(' -5 ') / 6
B( 2, 1) = TO_FM(' 25 ') / 18
B( 3, 0) = TO_FM(' 5 ') / 24
B( 3, 2) = TO_FM(' 5 ') / 8
B( 4, 0) = TO_FM(' 29 ') / 150
B( 4, 2) = TO_FM(' 11 ') / 50
B( 4, 3) = TO_FM(' -2 ') / 25
B( 5, 0) = TO_FM(' 1 ') / 10
B( 5, 3) = TO_FM(' 2 ') / 5
B( 5, 4) = TO_FM(' 1 ') / 2
B( 6, 0) = TO_FM(' .1034845616366797766729935465119103444997447982019713166066629728281981965079290745983 ')
B( 6, 3) = TO_FM(' .1220688873064072225896440828689620771395927148341621347412746563709055937325311521675 ')
B( 6, 4) = TO_FM(' .4825744903312466224751347801256881128659190238501680496794015023696413273862321544150 ')
B( 6, 5) = TO_FM(' -.3814096000156069997308862400056202056641130724784114774219699240039767479629669855696e-1 ')
B( 7, 0) = TO_FM(' .1243805266540944128815164208687993162684914663596714231632892354628068537117612942798 ')
B( 7, 4) = TO_FM(' .2261202821975843014222386629792029011967523207426331439651447460281196206643404356021 ')
B( 7, 5) = TO_FM(' .1378858876180808806076958370164778145309694174914933853635428709475288586061552782365e-1 ')
B( 7, 6) = TO_FM(' -.6722101339966844497493995074143058569500863415253821828561997825320849038679063596730e-1 ')
B( 8, 0) = TO_FM(' .9369190656596738155308854560830059338663496952177500856556033862893464429241815101000e-1 ')
B( 8, 5) = TO_FM(' -.6134068434505109872294989956416647356209145071288588710070986068372475355320835997035e-2 ')
B( 8, 6) = TO_FM(' .2160198256255030637088600976598665734909794332781173201886676706066128640340557614360 ')
B( 8, 7) = TO_FM(' .4236950635157619373376190739609767532058674695441235326831157041055522397561196508237 ')
B( 9, 0) = TO_FM(' .8384798124090526646169687913728140859805331392249111310693346670107922625197375034871e-1 ')
B( 9, 5) = TO_FM(' -.1179493671009738143197550560312957753679619605907361507776128268875265788248790903515e-1 ')
B( 9, 6) = TO_FM(' -.2472990205688126523394738387431945983259928403533401326974984247503501083158412965835 ')
B( 9, 7) = TO_FM(' .9780808583677290122593130140812916655037406554767339407565991037499621093437371932341e-1 ')
B( 9, 8) = TO_FM(' .2175906892434206313600086517678603183441681200247821768799893467069296630467914197921 ')
B(10, 0) = TO_FM(' .6152553597694282279545623896143147143334239690648211074539397569215087099333654844097e-1 ')
B(10, 5) = TO_FM(' .5922327803245033080429900057980465247383895604442571368349896773084347972825775455007e-2 ')
B(10, 6) = TO_FM(' .4703261599638411122172243032058941134553625307461088250108483236601604516650193568134 ')
B(10, 7) = TO_FM(' .2996888638486790008539818370961923991368311216717812791841936858888827504094204242461 ')
B(10, 8) = TO_FM(' -.2476568775939949146899922763298108258539580692639470955481886317480090967647905771626 ')
B(10, 9) = TO_FM(' .1108950297714376828939998518390617145224451736006787182086245987785252503880550245038 ')
B(11, 0) = TO_FM(' .4197000733627825798617928647872777872134836565431046112459945389674655429048057710370e-1 ')
B(11, 5) = TO_FM(' -.317987696266205093901912847692712407988609169703103952205634e-2 ')
B(11, 6) = TO_FM(' .8063977149061920772608217115203795063935431115674197501197468839656405367779525213500 ')
B(11, 7) = TO_FM(' .9759831264123889790935228506842888513146720480030545503571875185550549213299958241991e-1 ')
B(11, 8) = TO_FM(' .7785755781583989090275124464529272389997634605941819649588520345133050850477185489203 ')
B(11, 9) = TO_FM(' .2048904238315994281894992020981056033120292350814206535748293420400885242747823516625 ')
B(11,10) = TO_FM(' -1.562615796274681883070709439505278252114628922364243608928053762634922556160297217820 ')
B(12, 0) = TO_FM(' .4377267822337301635744652424953398116882149670716141232569729223172939742940416733395e-1 ')
B(12, 8) = TO_FM(' .6243650275201952087943586285809336252816312169030959172012504609444028241438248581173e-2 ')
B(12, 9) = TO_FM(' .2000430971095773149944351654696478568290662322182649696087680691197048872391143823078 ')
B(12,10) = TO_FM(' -.8053283678049830368238571620489029119233928873370293148442058928084075077460302544840e-2 ')
B(12,11) = TO_FM(' .2115175280673965219157119035233996013168778251575505730512208770404786743066139905871e-1 ')
B(13, 0) = TO_FM(' .2834992503635145630950235919207173122471376548964770977684956012393009143065795513785e-1 ')
B(13, 8) = TO_FM(' .2491632048558174075389491488059951494598846535854176800982219995075912885766744587193e-2 ')
B(13, 9) = TO_FM(' .2301387878545931496383998463737427687720871226381422342236583655735620108657836993957e-1 ')
B(13,10) = TO_FM(' -.3221559566929770987244760924671208781894636047606204610433085107190031098987004938258e-2 ')
B(13,11) = TO_FM(' .9884425494476646689463354144878852560408199827860146481292993078049373245839618405001e-2 ')
B(13,12) = TO_FM(' -.2130107713288873513843076428759273848866345654295724666320922464722154754985568313136e-1 ')
B(14, 0) = TO_FM(' .3435118942902430010494322347351479430833531749807014262686507474123120416010457867571 ')
B(14, 8) = TO_FM(' .2104519120236273856090970119990106557888074052256267000419050051487632641518018732685 ')
B(14, 9) = TO_FM(' 1.034274520572304119364829268288257099386679996983247401666929134177931632176349026735 ')
B(14,10) = TO_FM(' .6003036458644224870512404482066405749390780924061569454673075686417142117164254262878e-2 ')
B(14,11) = TO_FM(' .8559381250996195375780121060024077289150626526164160058172684354881277648341960563008 ')
B(14,12) = TO_FM(' -.9772350050367668108722648523725256330131076568928396776974412446349105799705851506077 ')
B(14,13) = TO_FM(' -.6600269804792946946162250138563276937205739812199748747775581736879654453322759683463 ')
B(15, 0) = TO_FM(' -.1435740016721680695382063999350763666577559543783998809757153672896315044426183882232e-1 ')
B(15, 8) = TO_FM(' -.3662532700490399702936857968489747917331190817335522078657913621382824038988807796287e-1 ')
B(15, 9) = TO_FM(' .3502549756362136819768494069798465243467890824711035742020654749717518291597210559354e-1 ')
B(15,10) = TO_FM(' .3609460163621135089317866587583352398236899298642376718895880083960486970547825683491e-1 ')
B(15,11) = TO_FM(' -.2652199675536811063515959468346019236496270124574642848667252606942739787160130682669e-1 ')
B(15,12) = TO_FM(' .4456990113056981196389115375088399081043363230822267716707629092315111479614958673268e-1 ')
B(15,13) = TO_FM(' .1243430933313582432862255957417864480389734088951067419167759990001419776217292554191 ')
B(15,14) = TO_FM(' .4138296932394806944035124962043359604261929086744760344472227418812310333088685698274e-2 ')
B(16, 0) = TO_FM(' .3560324044251202909756091163980891762641062223797488026536968101501275805051289760823 ')
B(16, 8) = TO_FM(' -.450192758947562595966821779075956175110645100214763601190349 ')
B(16, 9) = TO_FM(' .430527907083710898626656292808782917793030154094709462877146 ')
B(16,10) = TO_FM(' .5119730290110222376685569603940716920771257870306513863906805244405042813755411512463 ')
B(16,11) = TO_FM(' .9083036388864042603901591246381102139974962148199046305445452541870528153933236088278 ')
B(16,12) = TO_FM(' -1.239210933719339317573724691515340288544138892486057261860887966510000755220957594942 ')
B(16,13) = TO_FM(' -.6490486616717614651416723488790625539054028319671910976544025456235491510559878435372 ')
B(16,14) = TO_FM(' .2517089045868192922104805299489705414048878529314474912189256354259853776829630937658 ')
B(16,15) = TO_FM(' .7799064703455863988107567952823344760235405934115501870206452879298798513199886085571 ')
B(17, 0) = TO_FM(' .1309356874065130664068812064188349801274704382131924878449566575565302965696195341197e-1 ')
B(17,12) = TO_FM(' -.9320530679851139459084619627671082378586315096846671421247697017556505173897578610165e-4 ')
B(17,13) = TO_FM(' .5053743342622993596400904431385907267709423447161223817027456630856526555478831396014e-1 ')
B(17,14) = TO_FM(' .8044703419444879791095791096101977976413118689308653610493721999399129417586629251430e-6 ')
B(17,15) = TO_FM(' .5917260294941711905287557427777172598443409719243215281782302034071342229921661278343e-3 ')
B(17,16) = TO_FM(' -.4016147221545573370646916849063755877322642479500938046774565993013424294867398455789e-6 ')
B(18, 0) = TO_FM(' .2079264844660530125419445440007656521672552061443734079797586969853055549175505457737e-1 ')
B(18,12) = TO_FM(' .5826959188000859151019026978372841089514061030298715701031065480360641416298102920851e-3 ')
B(18,13) = TO_FM(' -.8017007323588159390833421865258527466405584659196335246554992680506588169863285718822e-2 ')
B(18,14) = TO_FM(' .4038476438471369403751708217435605704841172903308955066191655368223862388605213690921e-5 ')
B(18,15) = TO_FM(' .8546099980555061442250561145675356025101146220336224918025961310211940592009621595606e-1 ')
B(18,16) = TO_FM(' -.2044864809358042427067075696910043079044428375526774562331430989116458814609927891477e-5 ')
B(18,17) = TO_FM(' .1053285788244318933997994029790939973542409042351728431465827473723673651882417656762 ')
B(19, 0) = TO_FM(' 1.401534497957360214154462473557713067184864529175977331289881318884096354294079099114 ')
B(19,12) = TO_FM(' -.2302520009842212616162724103674156212611302982744556219175010157057031125814669239016 ')
B(19,13) = TO_FM(' -7.211068404669129056595822371068742471658564935099615697324849532576890894506619405031 ')
B(19,14) = TO_FM(' .3729015606948363352369953278521323402177595666786623882373057096229137360164435411243e-2 ')
B(19,15) = TO_FM(' -4.714154957271250206787781793922247570113233732218200980194845522013711035054762664884 ')
B(19,16) = TO_FM(' -.1763676575453492420538419950327976735749038866956001340593194717236122233799126229446e-2 ')
B(19,17) = TO_FM(' 7.641305480386987655630293108802376511851733678139370059818519661401442202665741111270 ')
B(19,18) = TO_FM(' 3.506020436597518349898960829497447109682129498933753736341591881470708008233521976557 ')
B(20, 0) = TO_FM(' 11.95146506941206867993723858307164016744736108265535168242754934626543968357331742096 ')
B(20,12) = TO_FM(' 7.794809321081759687835167002317643882202842795989809549197917776161588225206322580459 ')
B(20,13) = TO_FM(' -56.45013938673257925235609911209042814404681000613405538635967763011214022629172907669 ')
B(20,14) = TO_FM(' .9123763069306449013445304492902766457096074504036737047499704936582270274950128398912e-1 ')
B(20,15) = TO_FM(' -12.73362799254348862019455243091992750381627175299189605168457824373779389828110581300 ')
B(20,16) = TO_FM(' -.3968959219047197123135428109397366747123830704331478729319411886202118671113516172493e-1 ')
B(20,17) = TO_FM(' 54.43921418835708869962257651553077918614383784233053341001985423053366890118247056463 ')
B(20,18) = TO_FM(' -3.644116379215692368464069903613506458067214784092667356589342345057374050114156075061 ')
B(20,19) = TO_FM(' -.8045032499105099108990307879585794993156949132107878807481027183961246894903442258757 ')
B(21, 0) = TO_FM(' -148.8094265071004884278388682686476255619306120821485965777899951377767737092911763254 ')
B(21,12) = TO_FM(' -91.72952782912564843579356624023216234952287290363542836291360346578688265538801398361 ')
B(21,13) = TO_FM(' 707.6561449715983598345757192863357161548211289666495623584804744987957677893379157809 ')
B(21,14) = TO_FM(' -1.10563611857482440905296961311590930801338308942637769555540 ')
B(21,15) = TO_FM(' 176.1345918838113725878598980760556604069995167623016865882869129962911416096097878945 ')
B(21,16) = TO_FM(' .4913848242148806622688983451644545574168846314027647925019604519368994965045299923826 ')
B(21,17) = TO_FM(' -684.2780004498149443582375356108950819560771678936002751371799726829821841834791232605 ')
B(21,18) = TO_FM(' 27.99106049983982589842243321243804074460025184006686868209688958109916979926727384229 ')
B(21,19) = TO_FM(' 13.19397100302823334436709643711532384350641596237449753683872220663989495376087330358 ')
B(21,20) = TO_FM(' 1.251287812839804454501149741480560063172688300773964063605141347518040989702499199856 ')
B(22, 0) = TO_FM(' -9.673079469481967636441261184332193958399514085718772596349277868068021458303626779169 ')
B(22,12) = TO_FM(' -4.469901508585055314438462277019603604978306814087514357488023393670679083633020106516 ')
B(22,13) = TO_FM(' 45.51271286909526819682419504000527511789059078173984816890412459840121969200961260987 ')
B(22,14) = TO_FM(' -.713085086183826912791492024438246129930559805352394367050813e-1 ')
B(22,15) = TO_FM(' 11.22736140684127415825906244799393842078268007767944830815221105133516977144595052189 ')
B(22,16) = TO_FM(' .1262443767176227245162379129091388093617868898191054263714925416869147773104813482457 ')
B(22,17) = TO_FM(' -43.54393395494833136058106249072421076238143044676214056937881652359375369765457150165 ')
B(22,18) = TO_FM(' .7871743075430589783987929949965509020645460914432340378113766124779028133099797867162 ')
B(22,19) = TO_FM(' .5322646967446842156693007086038866907853957768215038536520118921656033723449302296244 ')
B(22,20) = TO_FM(' .4224227339963253260102251274713887725750865388096033468497941673910509540050957057177 ')
B(22,21) = TO_FM(' .8591312495030671073084380314998594434411150562941549563989586466154235621165245563192e-1 ')
B(23, 0) = TO_FM(' -10.06640324470547024033966069004268914722028247579687652710623604380152449409080444899 ')
B(23, 8) = TO_FM(' -.3662532700490399702936857968489747917331190817335522078657913621382824038988807796287e-1 ')
B(23, 9) = TO_FM(' .3502549756362136819768494069798465243467890824711035742020654749717518291597210559354e-1 ')
B(23,10) = TO_FM(' .3609460163621135089317866587583352398236899298642376718895880083960486970547825683491e-1 ')
B(23,11) = TO_FM(' -.2652199675536811063515959468346019236496270124574642848667252606942739787160130682669e-1 ')
B(23,12) = TO_FM(' -6.270889721814641435905531494788716038393561229573960230194057818533161624674313994502 ')
B(23,13) = TO_FM(' 48.20792374425629890907021030081950639234925931416361161278899187780407980462426656808 ')
B(23,14) = TO_FM(' -.694471689136165640882395180583732834557754169149088630301342e-1 ')
B(23,15) = TO_FM(' 12.68106902048502956983413709136098070661084838114121251454273060707937017246509534894 ')
B(23,16) = TO_FM(' .119671168968323754838161435501011294100927813964199613229864e-1 ')
B(23,17) = TO_FM(' -46.72497649924824080033582682426626955932013216597956070401309263301039263373634230581 ')
B(23,18) = TO_FM(' 1.330296133266267113147100392982165913990335111912271192356479099067512051132965697343 ')
B(23,19) = TO_FM(' 1.007667875033982983534389036199266577711627177936617199056121787956529680139072027935 ')
B(23,20) = TO_FM(' .2095120519336650916641223884754807028927707538644872411247284065032940106679251005781e-1 ')
B(23,21) = TO_FM(' .2101347063312641773177354243313964074244121884437574908902263894855162847478911411134e-1 ')
B(23,22) = TO_FM(' .9521960144171217941751015424545759073763602336583562405468424451848266905185171865534e-2 ')
B(24, 0) = TO_FM(' -409.4780816777437087725890974093703576244243416067520683455326035855162023776088699896 ')
B(24, 8) = TO_FM(' .2104519120236273856090970119990106557888074052256267000419050051487632641518018732685 ')
B(24, 9) = TO_FM(' 1.034274520572304119364829268288257099386679996983247401666929134177931632176349026735 ')
B(24,10) = TO_FM(' .6003036458644224870512404482066405749390780924061569454673075686417142117164254262878e-2 ')
B(24,11) = TO_FM(' .8559381250996195375780121060024077289150626526164160058172684354881277648341960563008 ')
B(24,12) = TO_FM(' -250.5169985474478604927776577293161303865840504207820779326393997812026874735614210230 ')
B(24,13) = TO_FM(' 1946.424666523884277660537503282647585958298508957614274560610260899186136259514015246 ')
B(24,14) = TO_FM(' -3.045038821023103655061058090868608827869505440976021016842196622317831446605499698935 ')
B(24,15) = TO_FM(' 490.6263795282817135212082652991680838415985422740616633051003594128766152337185220086 ')
B(24,16) = TO_FM(' 1.566475895312709071154840670135974457395956152459667753199388690841173424714434871921 ')
B(24,17) = TO_FM(' -1881.974289940111733622172673770358706192159066384530557689275696031792911993357071098 ')
B(24,18) = TO_FM(' 75.25922247248471752788377136433031498216206189142459440229301807516615379972994062700 ')
B(24,19) = TO_FM(' 34.57343569803310676224343447365546896967286447935510158001529990937243976348724448442 ')
B(24,20) = TO_FM(' 3.211476794409689614354173618470737551690229667488916278855754113243135684398993410117 ')
B(24,21) = TO_FM(' -.4604080417384143913072014042370588488672450952653828208427296561415079214017074427602 ')
B(24,22) = TO_FM(' -.8707183398418105224318841379579862457242520473889365722145748143125162133630944128398e-1 ')
B(24,23) = TO_FM(' -7.393518141583030675670169521955210639991857732491329543926346613193825315394087286297 ')
B(25, 0) = TO_FM(' 3.433474758535508789210934962575967811206238910720084588712755786644583035514752699598 ')
B(25, 8) = TO_FM(' .2491632048558174075389491488059951494598846535854176800982219995075912885766744587193e-2 ')
B(25, 9) = TO_FM(' .2301387878545931496383998463737427687720871226381422342236583655735620108657836993957e-1 ')
B(25,10) = TO_FM(' -.3221559566929770987244760924671208781894636047606204610433085107190031098987004938258e-2 ')
B(25,11) = TO_FM(' .9884425494476646689463354144878852560408199827860146481292993078049373245839618405001e-2 ')
B(25,12) = TO_FM(' 2.162527993779225077883078419047573540457592253357327094851479956564246957314476133478 ')
B(25,13) = TO_FM(' -16.26998645464574213280656406601394890069875520402288517985775075363232756881970486667 ')
B(25,14) = TO_FM(' -.1285345021205245528435834174709350105380290375426545062302651848844352856037884822181 ')
B(25,15) = TO_FM(' -8.98915042666504253089307820833379330486511746063552853023189 ')
B(25,16) = TO_FM(' -.3485953632320253333870802018510136501924017672505137649688730136175086767654181319387e-2 ')
B(25,17) = TO_FM(' 15.79361941133398075362351873886955741358533870251397376656158275266140525531011608606 ')
B(25,18) = TO_FM(' -.5744033309140950656281654820173358201483836631956754708231458398423255984252281047127 ')
B(25,19) = TO_FM(' -.3456020390213932966927224966081249825352372288276553067081833889419898565070467534157 ')
B(25,20) = TO_FM(' -.6622414902065850917316199913837577811330679927074186873906450413385445874036001388495e-2 ')
B(25,21) = TO_FM(' -.7777881292422041640325464586073643097593472096267591120155367761150273183248441708392e-2 ')
B(25,22) = TO_FM(' -.3560841924022749133388272326974373646752408187917065879526063406092336300493607300593e-2 ')
B(25,23) = TO_FM(' 4.792825064499307996497977496298401894572969341393590555417712618624354747222657791607 ')
B(25,24) = TO_FM(' .153725464873068577844576387402512082757034273069877432944621 ')
B(26, 0) = TO_FM(' 32.30385208719854423269947344400315350913649750477846297617061421719281146058139852238 ')
B(26, 5) = TO_FM(' -.317987696266205093901912847692712407988609169703103952205634e-2 ')
B(26, 6) = TO_FM(' .8063977149061920772608217115203795063935431115674197501197468839656405367779525213500 ')
B(26, 7) = TO_FM(' .9759831264123889790935228506842888513146720480030545503571875185550549213299958241991e-1 ')
B(26, 8) = TO_FM(' .7785755781583989090275124464529272389997634605941819649588520345133050850477185489203 ')
B(26, 9) = TO_FM(' .2048904238315994281894992020981056033120292350814206535748293420400885242747823516625 ')
B(26,10) = TO_FM(' -1.562615796274681883070709439505278252114628922364243608928053762634922556160297217820 ')
B(26,12) = TO_FM(' 16.34298918823105706485042439739271747087533535041545512917666902744198799725970841669 ')
B(26,13) = TO_FM(' -154.5445552935436212307301896314710363993166836696091165017078152549564923882084122674 ')
B(26,14) = TO_FM(' 1.569710887033348726920342834176217614662635935824970859658624964687079589089479471888 ')
B(26,15) = TO_FM(' 3.276855450872481313214298172699007311655224049747336000450385269517693130775985884604 ')
B(26,16) = TO_FM(' -.5034892451936531763480407271997836265340810956916323972462042700071863164675818955838e-1 ')
B(26,17) = TO_FM(' 153.3211518580416650705937678859146940112243631025945564907021486707139114294996134941 ')
B(26,18) = TO_FM(' 7.175681863277204958467664848147841435678263080348653386540185145833155908488128910568 ')
B(26,19) = TO_FM(' -2.940367486753004819459176598969309892153205943807775979427615740476908865098135595635 ')
B(26,20) = TO_FM(' -.6658459460768031444707496760226288702819204931972568878708744783028558369468497032253e-1 ')
B(26,21) = TO_FM(' -.4623460549908436612292486685622172611769665140168592842374268449140643068786760618896e-1 ')
B(26,22) = TO_FM(' -.2041987335856794015393882286172697788485797748215817776751235910664984352284968100100e-1 ')
B(26,23) = TO_FM(' -53.35231064387358505159534411659981079740450904957915977996876390672711239156977103431 ')
B(26,24) = TO_FM(' -1.355487147150786549787321867059964040175545016141913251148206738329360142936656282958 ')
B(26,25) = TO_FM(' -1.571962758012327518829017351714592491776872191144425834618663282570958684038698495739 ')
B(27, 0) = TO_FM(' -16.64514674863415128720312944039317587645603711308189782044257016154825923946758475845 ')
B(27, 5) = TO_FM(' .5922327803245033080429900057980465247383895604442571368349896773084347972825775455007e-2 ')
B(27, 6) = TO_FM(' .4703261599638411122172243032058941134553625307461088250108483236601604516650193568134 ')
B(27, 7) = TO_FM(' .2996888638486790008539818370961923991368311216717812791841936858888827504094204242461 ')
B(27, 8) = TO_FM(' -.2476568775939949146899922763298108258539580692639470955481886317480090967647905771626 ')
B(27, 9) = TO_FM(' .1108950297714376828939998518390617145224451736006787182086245987785252503880550245038 ')
B(27,11) = TO_FM(' -.4917190438462291470706666287041940976780819072106730449888664749836403474888832394921 ')
B(27,12) = TO_FM(' -11.47431544272894969683894925643525363508424541308531757856483965863898534849416840511 ')
B(27,13) = TO_FM(' 80.25931665762302725417024858864844001527933666235899875893849400507278534931158408231 ')
B(27,14) = TO_FM(' -.3841323039800428476253125267590291037469268413420882192068133107492120348263618466046 ')
B(27,15) = TO_FM(' 7.281476674681075834713269509261361157676125818628777243483988994104498714011047355205 ')
B(27,16) = TO_FM(' -.1326993846122483795105717081760352748368273416167518843018178653526280269065470590467 ')
B(27,17) = TO_FM(' -81.07998325257307266746792897522552400060707166336329885641562357237166810196760593013 ')
B(27,18) = TO_FM(' -1.250374928356206395217681856561791199622537474924031863192434629401819729868852090550 ')
B(27,19) = TO_FM(' 2.592635949695436810237763795043773249942264473592968880837586883560068434349818491911 ')
B(27,20) = TO_FM(' -.3014402983464045398301639972605268752644315372756414953420797074457552586137488110716 ')
B(27,21) = TO_FM(' .2213844607898323374517064515727737916952468390573184143179573617704323166985265217363 ')
B(27,22) = TO_FM(' .8275772747718929319559898709746931529962764354298098905497078729734353980896315305691e-1 ')
B(27,23) = TO_FM(' 18.99606620406115204646724500372432639981751614122371589366718674999943569769696943522 ')
B(27,24) = TO_FM(' .2692319464096396856234680151283341674600519103489128451211866688910668614577677735665 ')
B(27,25) = TO_FM(' 1.626748274470665374629893649296289339881250292841836802790201430504847697803528636395 ')
B(27,26) = TO_FM(' .4917190438462291470706666287041940976780819072106730449888664749836403474888832394921 ')
B(28, 0) = TO_FM(' .8384798124090526646169687913728140859805331392249111310693346670107922625197375034871e-1 ')
B(28, 5) = TO_FM(' -.1179493671009738143197550560312957753679619605907361507776128268875265788248790903515e-1 ')
B(28, 6) = TO_FM(' -.2472990205688126523394738387431945983259928403533401326974984247503501083158412965835 ')
B(28, 7) = TO_FM(' .9780808583677290122593130140812916655037406554767339407565991037499621093437371932341e-1 ')
B(28, 8) = TO_FM(' .2175906892434206313600086517678603183441681200247821768799893467069296630467914197921 ')
B(28,10) = TO_FM(' .1375856067633252248656596321967877466474472229750848659754400903987833771639575727867 ')
B(28,11) = TO_FM(' .4398702297150466850587900923415450260461038902942613590425808839943205635447284745074e-1 ')
B(28,13) = TO_FM(' -.5137008137681933419570044566186303037387573636419640300869712169933398305905931343468 ')
B(28,14) = TO_FM(' .8263556911513155086442113083991534587014231586161685769224194977471882335420141183213 ')
B(28,15) = TO_FM(' 25.70181397198118326258738829725199395111365563419600781824702737091645129169813134401 ')
B(28,23) = TO_FM(' -25.70181397198118326258738829725199395111365563419600781824702737091645129169813134401 ')
B(28,24) = TO_FM(' -.8263556911513155086442113083991534587014231586161685769224194977471882335420141183213 ')
B(28,25) = TO_FM(' .5137008137681933419570044566186303037387573636419640300869712169933398305905931343468 ')
B(28,26) = TO_FM(' -.4398702297150466850587900923415450260461038902942613590425808839943205635447284745074e-1 ')
B(28,27) = TO_FM(' -.1375856067633252248656596321967877466474472229750848659754400903987833771639575727867 ')
B(29, 0) = TO_FM(' .1243805266540944128815164208687993162684914663596714231632892354628068537117612942798 ')
B(29, 4) = TO_FM(' .2261202821975843014222386629792029011967523207426331439651447460281196206643404356021 ')
B(29, 5) = TO_FM(' .1378858876180808806076958370164778145309694174914933853635428709475288586061552782365e-1 ')
B(29, 6) = TO_FM(' -.6722101339966844497493995074143058569500863415253821828561997825320849038679063596730e-1 ')
B(29, 9) = TO_FM(' -.8562389750854283547553497698795017721121215974115638028550665385850612741040225222977 ')
B(29,10) = TO_FM(' -1.963375228668589089282628500280938139881804405182674045535756631526916950083353845169 ')
B(29,11) = TO_FM(' -.2323328227241194012372462573089218472501081992304199949782180319905262045718872259601 ')
B(29,13) = TO_FM(' 4.306607190864533494616689368765629477724325620534780926267640393608500758570100495873 ')
B(29,14) = TO_FM(' -2.927229632494654826597879112023904466876873949506336126307786635262992367484998786517 ')
B(29,15) = TO_FM(' -82.31316663978589444544923341054587077357619664281386893950601309356417181948645997040 ')
B(29,23) = TO_FM(' 82.31316663978589444544923341054587077357619664281386893950601309356417181948645997040 ')
B(29,24) = TO_FM(' 2.927229632494654826597879112023904466876873949506336126307786635262992367484998786517 ')
B(29,25) = TO_FM(' -4.306607190864533494616689368765629477724325620534780926267640393608500758570100495873 ')
B(29,26) = TO_FM(' .2323328227241194012372462573089218472501081992304199949782180319905262045718872259601 ')
B(29,27) = TO_FM(' 1.963375228668589089282628500280938139881804405182674045535756631526916950083353845169 ')
B(29,28) = TO_FM(' .8562389750854283547553497698795017721121215974115638028550665385850612741040225222977 ')
B(30, 0) = TO_FM(' .1034845616366797766729935465119103444997447982019713166066629728281981965079290745983 ')
B(30, 3) = TO_FM(' .1220688873064072225896440828689620771395927148341621347412746563709055937325311521675 ')
B(30, 4) = TO_FM(' .4825744903312466224751347801256881128659190238501680496794015023696413273862321544150 ')
B(30, 5) = TO_FM(' -.3814096000156069997308862400056202056641130724784114774219699240039767479629669855696e-1 ')
B(30, 7) = TO_FM(' -.5504995253108023241383885070205081774114143110000375617128363206424473498745141065969 ')
B(30, 9) = TO_FM(' -.7119158115851892278876482620437943875782918824067455704957652139710574799878630163853 ')
B(30,10) = TO_FM(' -.5841296056715513404329887301584808720953353296452275957070524410065417676683463009109 ')
B(30,13) = TO_FM(' 2.110463081258649321287173000466227503003750542789369878507182287710881470618943318741 ')
B(30,14) = TO_FM(' -.8374947367395721355257420230010379926952601753351235177405529298334532793741463162845e-1 ')
B(30,15) = TO_FM(' 5.100214990723209140752959690433441131075450608628042491597346388445135412965217165555 ')
B(30,23) = TO_FM(' -5.100214990723209140752959690433441131075450608628042491597346388445135412965217165555 ')
B(30,24) = TO_FM(' .8374947367395721355257420230010379926952601753351235177405529298334532793741463162845e-1 ')
B(30,25) = TO_FM(' -2.110463081258649321287173000466227503003750542789369878507182287710881470618943318741 ')
B(30,27) = TO_FM(' .5841296056715513404329887301584808720953353296452275957070524410065417676683463009109 ')
B(30,28) = TO_FM(' .7119158115851892278876482620437943875782918824067455704957652139710574799878630163853 ')
B(30,29) = TO_FM(' .5504995253108023241383885070205081774114143110000375617128363206424473498745141065969 ')
B(31, 0) = TO_FM(' 29 ') / 150
B(31, 2) = TO_FM(' 11 ') / 50
B(31, 3) = TO_FM(' -2 ') / 25
B(31, 6) = TO_FM(' .1099934255807247039194624048650683408451190582958464264636524271459687549994002654752 ')
B(31, 7) = TO_FM(' -.2542970480762701613840685069971531221418356269767039208462421656164179875269042982442 ')
B(31, 9) = TO_FM(' .8655707771166942543437703438210982818328474012330118593467368132762510892051242759318 ')
B(31,10) = TO_FM(' 3.324164491140930831067995527865720183368600929369864071601998386039920635781409865040 ')
B(31,13) = TO_FM(' -12.01022233159779338823523851486618412603019426339968151272769528462035002110216728101 ')
B(31,14) = TO_FM(' .4766014662424932394304427768620618996029637820035802094825720242694315551196576125507 ')
B(31,15) = TO_FM(' -29.02430112210363905258026232136540995962512213324709106915239870601916450708546744075 ')
B(31,23) = TO_FM(' 29.02430112210363905258026232136540995962512213324709106915239870601916450708546744075 ')
B(31,24) = TO_FM(' -.4766014662424932394304427768620618996029637820035802094825720242694315551196576125507 ')
B(31,25) = TO_FM(' 12.01022233159779338823523851486618412603019426339968151272769528462035002110216728101 ')
B(31,27) = TO_FM(' -3.324164491140930831067995527865720183368600929369864071601998386039920635781409865040 ')
B(31,28) = TO_FM(' -.8655707771166942543437703438210982818328474012330118593467368132762510892051242759318 ')
B(31,29) = TO_FM(' .2542970480762701613840685069971531221418356269767039208462421656164179875269042982442 ')
B(31,30) = TO_FM(' -.1099934255807247039194624048650683408451190582958464264636524271459687549994002654752 ')
B(32, 0) = TO_FM(' -5 ') / 6
B(32, 1) = TO_FM(' 25 ') / 18
B(32, 4) = TO_FM(' -3 ') / 4
B(32, 6) = TO_FM(' -.4925295437180263044226820491140213202002146815806577847190740839644346370048749342561 ')
B(32,30) = TO_FM(' .4925295437180263044226820491140213202002146815806577847190740839644346370048749342561 ')
B(32,31) = TO_FM(' 3 ') / 4
B(33, 0) = TO_FM(' 1 ') / 9
B(33, 2) = TO_FM(' -2 ') / 9
B(33,32) = TO_FM(' 2 ') / 9
B(34, 0) = TO_FM(' .2858351403889715587960888421638364148529275378945964668924322897553490152559792262023 ')
B(34, 1) = TO_FM(' 7 ') / 24
B(34, 2) = TO_FM(' 7 ') / 32
B(34, 4) = TO_FM(' 21 ') / 128
B(34, 6) = TO_FM(' .2181943549455566583271882415813521070932888243221879411415164327116967439531911272777 ')
B(34, 7) = TO_FM(' .1803928984786977668636352219467754377196200536418492285624347210514163759703679527180 ')
B(34, 9) = TO_FM(' .2057138394048450188591207551229295422775700949828089053939914789386228504942804843989 ')
B(34,10) = TO_FM(' .2427157915817702399702829279594465157627459713866705419485763522859549196625913978401 ')
B(34,11) = TO_FM(' .2464657808136293058336092911818914077992281038693057051370210135284213379790417930740 ')
B(34,12) = TO_FM(' -3.449919407908908249798341546016226620603704606149316442883265523381128452524989278943 ')
B(34,13) = TO_FM(' .2288755621600360817607290607384585842942203725527402184592948392511281334278617959957 ')
B(34,14) = TO_FM(' .2832905997021514153215274190567333359784365954938557898314048426595070708424182066065 ')
B(34,15) = TO_FM(' 3.210851258377666409601314905442367870055573203322387098512984999880577120008173123283 ')
B(34,16) = TO_FM(' -.2235387773648456999202337562141625079641252300836740320899016275445898395177373582441 ')
B(34,17) = TO_FM(' -.7071211572044190735187272862074872121300912319552061607910521928571247612111795934106 ')
B(34,18) = TO_FM(' 3.211233451502870804081747292028565008932600344430223743249588034157195885590228893622 ')
B(34,19) = TO_FM(' 1.409543483096697660304144743011231757690459455735489863573218752821178310978199657967 ')
B(34,20) = TO_FM(' -.1513620534437426131216022767425181110909630262036760559494590353712667648924754181285 ')
B(34,21) = TO_FM(' .3723505745270142764547240802146199843971210282021482987373568243836683323798121465643 ')
B(34,22) = TO_FM(' .2529787464063613367221999077621412859157757281294143192610824780367182739421617243696 ')
B(34,23) = TO_FM(' -3.210851258377666409601314905442367870055573203322387098512984999880577120008173123283 ')
B(34,24) = TO_FM(' -.2832905997021514153215274190567333359784365954938557898314048426595070708424182066065 ')
B(34,25) = TO_FM(' -.2288755621600360817607290607384585842942203725527402184592948392511281334278617959957 ')
B(34,26) = TO_FM(' -.2464657808136293058336092911818914077992281038693057051370210135284213379790417930740 ')
B(34,27) = TO_FM(' -.2427157915817702399702829279594465157627459713866705419485763522859549196625913978401 ')
B(34,28) = TO_FM(' -.2057138394048450188591207551229295422775700949828089053939914789386228504942804843989 ')
B(34,29) = TO_FM(' -.1803928984786977668636352219467754377196200536418492285624347210514163759703679527180 ')
B(34,30) = TO_FM(' -.2181943549455566583271882415813521070932888243221879411415164327116967439531911272777 ')
B(34,31) = TO_FM(' -21 ') / 128
B(34,32) = TO_FM(' -7 ') / 32
B(34,33) = TO_FM(' -7 ') / 24
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_RK14_COEFFS
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