Create the actual Adams-Bashforth integrator: initialize the b coefficients.
If the integrator is initialized with a bad (unsupported) number of required time steps the initialization fails and the integrator error status is updated consistently for external-provided errors handling.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(integrator_adams_bashforth), | intent(inout) | :: | self | Integrator. |
||
| character(len=*), | intent(in) | :: | scheme | Selected scheme. |
||
| logical, | intent(in), | optional | :: | autoupdate | Enable cyclic autoupdate of previous time steps. |
|
| class(integrand_object), | intent(in), | optional | :: | U | Integrand molding prototype. |
|
| logical, | intent(in), | optional | :: | stop_on_fail | Stop execution if initialization fail. |
subroutine initialize(self, scheme, autoupdate, U, stop_on_fail)
!< Create the actual Adams-Bashforth integrator: initialize the *b* coefficients.
!<
!< @note If the integrator is initialized with a bad (unsupported) number of required time steps the initialization fails and
!< the integrator error status is updated consistently for external-provided errors handling.
class(integrator_adams_bashforth), intent(inout) :: self !< Integrator.
character(*), intent(in) :: scheme !< Selected scheme.
logical, intent(in), optional :: autoupdate !< Enable cyclic autoupdate of previous time steps.
class(integrand_object), intent(in), optional :: U !< Integrand molding prototype.
logical, intent(in), optional :: stop_on_fail !< Stop execution if initialization fail.
if (self%is_supported(scheme=scheme)) then
call self%destroy
self%description_ = trim(adjustl(scheme))
select case(trim(adjustl(scheme)))
case('adams_bashforth_1')
self%steps = 1 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 1.0_R_P
case('adams_bashforth_2')
self%steps = 2 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -1.0_R_P/2.0_R_P
self%b(2) = 3.0_R_P/2.0_R_P
case('adams_bashforth_3')
self%steps = 3 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 5.0_R_P/12.0_R_P
self%b(2) = -16.0_R_P/12.0_R_P
self%b(3) = 23.0_R_P/12.0_R_P
case('adams_bashforth_4')
self%steps = 4 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -9.0_R_P/24.0_R_P
self%b(2) = 37.0_R_P/24.0_R_P
self%b(3) = -59.0_R_P/24.0_R_P
self%b(4) = 55.0_R_P/24.0_R_P
case('adams_bashforth_5')
self%steps = 5 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 251.0_R_P/720.0_R_P
self%b(2) = -1274.0_R_P/720.0_R_P
self%b(3) = 2616.0_R_P/720.0_R_P
self%b(4) = -2774.0_R_P/720.0_R_P
self%b(5) = 1901.0_R_P/720.0_R_P
case('adams_bashforth_6')
self%steps = 6 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -475.0_R_P/1440.0_R_P
self%b(2) = 2877.0_R_P/1440.0_R_P
self%b(3) = -7298.0_R_P/1440.0_R_P
self%b(4) = 9982.0_R_P/1440.0_R_P
self%b(5) = -7923.0_R_P/1440.0_R_P
self%b(6) = 4277.0_R_P/1440.0_R_P
case('adams_bashforth_7')
self%steps = 7 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 19087.0_R_P/60480.0_R_P
self%b(2) = -134472.0_R_P/60480.0_R_P
self%b(3) = 407139.0_R_P/60480.0_R_P
self%b(4) = -688256.0_R_P/60480.0_R_P
self%b(5) = 705549.0_R_P/60480.0_R_P
self%b(6) = -447288.0_R_P/60480.0_R_P
self%b(7) = 198721.0_R_P/60480.0_R_P
case('adams_bashforth_8')
self%steps = 8 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -36799.0_R_P/120960.0_R_P
self%b(2) = 295767.0_R_P/120960.0_R_P
self%b(3) = -1041723.0_R_P/120960.0_R_P
self%b(4) = 2102243.0_R_P/120960.0_R_P
self%b(5) = -2664477.0_R_P/120960.0_R_P
self%b(6) = 2183877.0_R_P/120960.0_R_P
self%b(7) = -1152169.0_R_P/120960.0_R_P
self%b(8) = 434241.0_R_P/120960.0_R_P
case('adams_bashforth_9')
self%steps = 9 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 1070017.0_R_P/3628800.0_R_P
self%b(2) = -9664106.0_R_P/3628800.0_R_P
self%b(3) = 38833486.0_R_P/3628800.0_R_P
self%b(4) = -91172642.0_R_P/3628800.0_R_P
self%b(5) = 137968480.0_R_P/3628800.0_R_P
self%b(6) = -139855262.0_R_P/3628800.0_R_P
self%b(7) = 95476786.0_R_P/3628800.0_R_P
self%b(8) = -43125206.0_R_P/3628800.0_R_P
self%b(9) = 14097247.0_R_P/3628800.0_R_P
case('adams_bashforth_10')
self%steps = 10 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -2082753.0_R_P/7257600.0_R_P
self%b(2) = 20884811.0_R_P/7257600.0_R_P
self%b(3) = -94307320.0_R_P/7257600.0_R_P
self%b(4) = 252618224.0_R_P/7257600.0_R_P
self%b(5) = -444772162.0_R_P/7257600.0_R_P
self%b(6) = 538363838.0_R_P/7257600.0_R_P
self%b(7) = -454661776.0_R_P/7257600.0_R_P
self%b(8) = 265932680.0_R_P/7257600.0_R_P
self%b(9) = -104995189.0_R_P/7257600.0_R_P
self%b(10) = 30277247.0_R_P/7257600.0_R_P
case('adams_bashforth_11')
self%steps = 11 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 134211265.0_R_P/479001600.0_R_P
self%b(2) = -1479574348.0_R_P/479001600.0_R_P
self%b(3) = 7417904451.0_R_P/479001600.0_R_P
self%b(4) = -22329634920.0_R_P/479001600.0_R_P
self%b(5) = 44857168434.0_R_P/479001600.0_R_P
self%b(6) = -63176201472.0_R_P/479001600.0_R_P
self%b(7) = 63716378958.0_R_P/479001600.0_R_P
self%b(8) = -46113029016.0_R_P/479001600.0_R_P
self%b(9) = 23591063805.0_R_P/479001600.0_R_P
self%b(10) = -8271795124.0_R_P/479001600.0_R_P
self%b(11) = 2132509567.0_R_P/479001600.0_R_P
case('adams_bashforth_12')
self%steps = 12 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -262747265.0_R_P/958003200.0_R_P
self%b(2) = 3158642445.0_R_P/958003200.0_R_P
self%b(3) = -17410248271.0_R_P/958003200.0_R_P
self%b(4) = 58189107627.0_R_P/958003200.0_R_P
self%b(5) = -131365867290.0_R_P/958003200.0_R_P
self%b(6) = 211103573298.0_R_P/958003200.0_R_P
self%b(7) = -247741639374.0_R_P/958003200.0_R_P
self%b(8) = 214139355366.0_R_P/958003200.0_R_P
self%b(9) = -135579356757.0_R_P/958003200.0_R_P
self%b(10) = 61633227185.0_R_P/958003200.0_R_P
self%b(11) = -19433810163.0_R_P/958003200.0_R_P
self%b(12) = 4527766399.0_R_P/958003200.0_R_P
case('adams_bashforth_13')
self%steps = 13 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 703604254357.0_R_P/2615348736000.0_R_P
self%b(2) = -9160551085734.0_R_P/2615348736000.0_R_P
self%b(3) = 55060974662412.0_R_P/2615348736000.0_R_P
self%b(4) = -202322913738370.0_R_P/2615348736000.0_R_P
self%b(5) = 507140369728425.0_R_P/2615348736000.0_R_P
self%b(6) = -915883387152444.0_R_P/2615348736000.0_R_P
self%b(7) = 1226443086129408.0_R_P/2615348736000.0_R_P
self%b(8) = -1233589244941764.0_R_P/2615348736000.0_R_P
self%b(9) = 932884546055895.0_R_P/2615348736000.0_R_P
self%b(10) = -524924579905150.0_R_P/2615348736000.0_R_P
self%b(11) = 214696591002612.0_R_P/2615348736000.0_R_P
self%b(12) = -61497552797274.0_R_P/2615348736000.0_R_P
self%b(13) = 13064406523627.0_R_P/2615348736000.0_R_P
case('adams_bashforth_14')
self%steps = 14 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -1382741929621.0_R_P/5230697472000.0_R_P
self%b(2) = 19382853593787.0_R_P/5230697472000.0_R_P
self%b(3) = -126174972681906.0_R_P/5230697472000.0_R_P
self%b(4) = 505586141196430.0_R_P/5230697472000.0_R_P
self%b(5) = -1393306307155755.0_R_P/5230697472000.0_R_P
self%b(6) = 2793869602879077.0_R_P/5230697472000.0_R_P
self%b(7) = -4204551925534524.0_R_P/5230697472000.0_R_P
self%b(8) = 4825671323488452.0_R_P/5230697472000.0_R_P
self%b(9) = -4246767353305755.0_R_P/5230697472000.0_R_P
self%b(10) = 2854429571790805.0_R_P/5230697472000.0_R_P
self%b(11) = -1445313351681906.0_R_P/5230697472000.0_R_P
self%b(12) = 537247052515662.0_R_P/5230697472000.0_R_P
self%b(13) = -140970750679621.0_R_P/5230697472000.0_R_P
self%b(14) = 27511554976875.0_R_P/5230697472000.0_R_P
case('adams_bashforth_15')
self%steps = 15 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = 8164168737599.0_R_P/31384184832000.0_R_P
self%b(2) = -122594813904112.0_R_P/31384184832000.0_R_P
self%b(3) = 859236476684231.0_R_P/31384184832000.0_R_P
self%b(4) = -3728807256577472.0_R_P/31384184832000.0_R_P
self%b(5) = 11205849753515179.0_R_P/31384184832000.0_R_P
self%b(6) = -24704503655607728.0_R_P/31384184832000.0_R_P
self%b(7) = 41280216336284259.0_R_P/31384184832000.0_R_P
self%b(8) = -53246738660646912.0_R_P/31384184832000.0_R_P
self%b(9) = 53471026659940509.0_R_P/31384184832000.0_R_P
self%b(10) = -41825269932507728.0_R_P/31384184832000.0_R_P
self%b(11) = 25298910337081429.0_R_P/31384184832000.0_R_P
self%b(12) = -11643637530577472.0_R_P/31384184832000.0_R_P
self%b(13) = 3966421670215481.0_R_P/31384184832000.0_R_P
self%b(14) = -960122866404112.0_R_P/31384184832000.0_R_P
self%b(15) = 173233498598849.0_R_P/31384184832000.0_R_P
case('adams_bashforth_16')
self%steps = 16 ; allocate(self%b(1:self%steps)) ; self%b = 0.0_R_P
self%b(1) = -16088129229375.0_R_P/62768369664000.0_R_P
self%b(2) = 257650275915823.0_R_P/62768369664000.0_R_P
self%b(3) = -1934443196892599.0_R_P/62768369664000.0_R_P
self%b(4) = 9038571752734087.0_R_P/62768369664000.0_R_P
self%b(5) = -29417910911251819.0_R_P/62768369664000.0_R_P
self%b(6) = 70724351582843483.0_R_P/62768369664000.0_R_P
self%b(7) = -129930094104237331.0_R_P/62768369664000.0_R_P
self%b(8) = 186087544263596643.0_R_P/62768369664000.0_R_P
self%b(9) = -210020588912321949.0_R_P/62768369664000.0_R_P
self%b(10) = 187463140112902893.0_R_P/62768369664000.0_R_P
self%b(11) = -131963191940828581.0_R_P/62768369664000.0_R_P
self%b(12) = 72558117072259733.0_R_P/62768369664000.0_R_P
self%b(13) = -30607373860520569.0_R_P/62768369664000.0_R_P
self%b(14) = 9622096909515337.0_R_P/62768369664000.0_R_P
self%b(15) = -2161567671248849.0_R_P/62768369664000.0_R_P
self%b(16) = 362555126427073.0_R_P/62768369664000.0_R_P
endselect
self%autoupdate = .true. ; if (present(autoupdate)) self%autoupdate = autoupdate
self%registers = self%steps
if (present(U)) call self%allocate_integrand_members(U=U)
else
call self%trigger_error(error=ERROR_UNSUPPORTED_SCHEME, &
error_message='"'//trim(adjustl(scheme))//'" unsupported scheme', &
is_severe=stop_on_fail)
endif
endsubroutine initialize