I1a1. Initial value problem of ordinary differential equations (for non-stiff problem)

Functions
Sub	Deabm (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, RTol() As Double, ATol() As Double, Info As Long, Optional Mode As Long=-1, Optional ITstop As Long=-1, Optional Tstop As Double)
	Initial value problem of ordinary differential equations (1~12-th order Adams-Bashforth-Moulton predictor-corrector method)
Sub	Deabm_r (N As Long, T As Double, Y() As Double, Tout As Double, RTol() As Double, ATol() As Double, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Mode As Long=-1, Optional ITstop As Long=-1, Optional Tstop As Double)
	Initial value problem of ordinary differential equations (1~12-th order Adams-Bashforth-Moulton predictor-corrector method) (reverse communication version)
Sub	Derkfa (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0)
	Initial value problem of a system of first order ordinary differential equations (5(4)-th order Runge-Kutta-Fehlberg method)
Sub	Derkfa_r (N As Long, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0)
	Initial value problem of a system of first order ordinary differential equations (5(4)-th order Runge-Kutta-Fehlberg method) (Reverse communication version)
Sub	Dop853a (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Nstiff As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0, Optional Beta As Double=0)
	Initial value problem of ordinary differential equations (8(5,3)-th order Dorman-Prince method)
Sub	Dop853a_r (N As Long, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Nstiff As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0, Optional Beta As Double=0)
	Initial value problem of ordinary differential equations (8(5,3)-th order Dorman-Prince method) (Reverse communication version)
Sub	Dopn1210 (N As Long, F2 As LongPtr, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (12(10)-th order Runge-Kutta-Nystrom method) (for second order differential equations)
Sub	Dopn1210_r (N As Long, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYpp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (12(10)-th order Runge-Kutta-Nystrom method) (for second order differential equations) (Reverse communication version)
Sub	Dopn43 (N As Long, F2 As LongPtr, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (4(3)-th order Runge-Kutta-Nystrom method) (for second order differential equations)
Sub	Dopn43_r (N As Long, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYpp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (4(3)-th order Runge-Kutta-Nystrom method) (for second order differential equations) (Reverse communication version)
Sub	Dopn64 (N As Long, F2 As LongPtr, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (6(4)-th order Runge-Kutta-Nystrom method) (for second order differential equations)
Sub	Dopn64_r (N As Long, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYpp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (6(4)-th order Runge-Kutta-Nystrom method) (for second order differential equations) (Reverse communication version)
Sub	Dopn86 (N As Long, F2 As LongPtr, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (8(6)-th order Runge-Kutta-Nystrom method) (for second order differential equations)
Sub	Dopn86_r (N As Long, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYpp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0)
	Initial value problem of ordinary differential equations (8(6)-th order Runge-Kutta-Nystrom method) (for second order differential equations) (Reverse communication version)
Sub	Dopri5a (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Nstiff As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0, Optional Beta As Double=0)
	Initial value problem of ordinary differential equations (5(4)-th order Dorman-Prince method)
Sub	Dopri5a_r (N As Long, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Nstiff As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0, Optional Beta As Double=0)
	Initial value problem of ordinary differential equations (5(4)-th order Dorman-Prince method) (Reverse communication version)
Sub	Dverka (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, Tend As Double, Tol As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Hmin As Double=0, Optional Scal As Double=0, Optional Efloor As Double=0)
	Initial value problem of ordinary differential equations (6(5)-th order Runge-Kutta-Verner method)
Sub	Dverka_r (N As Long, T As Double, Y() As Double, Tout As Double, Tend As Double, Tol As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional ErrCntl As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Hmin As Double=0, Optional Scal As Double=0, Optional Efloor As Double=0)
	Initial value problem of ordinary differential equations (6(5)-th order Runge-Kutta-Verner method) (Reverse communication version)
Sub	Odex2a (N As Long, F2 As LongPtr, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, Rtol() As Double, Atol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Km As Long=0, Optional Nsequ As Long=0, Optional Mudif As Long=0, Optional Iderr As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Fac3 As Double=0, Optional Fac4 As Double=0, Optional Safe1 As Double=0, Optional Safe2 As Double=0, Optional Safe3 As Double=0)
	Initial value problem of second order ordinary differential equations (extrapolation method)
Sub	Odex2a_r (N As Long, T As Double, Y() As Double, Yp() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYpp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Km As Long=0, Optional Nsequ As Long=0, Optional Mudif As Long=0, Optional Iderr As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Fac3 As Double=0, Optional Fac4 As Double=0, Optional Safe1 As Double=0, Optional Safe2 As Double=0, Optional Safe3 As Double=0)
	Initial value problem of second order ordinary differential equations (extrapolation method) (Reverse communication version)
Sub	Odexa (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Km As Long=0, Optional Nsequ As Long=0, Optional Mstab As Long=0, Optional Jstab As Long=0, Optional Mudif As Long=0, Optional Iderr As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Fac3 As Double=0, Optional Fac4 As Double=0, Optional Safe1 As Double=0, Optional Safe2 As Double=0, Optional Safe3 As Double=0)
	Initial value problem of ordinary differential equations (extrapolation method (GBS algorithm))
Sub	Odexa_r (N As Long, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Km As Long=0, Optional Nsequ As Long=0, Optional Mstab As Long=0, Optional Jstab As Long=0, Optional Mudif As Long=0, Optional Iderr As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Fac3 As Double=0, Optional Fac4 As Double=0, Optional Safe1 As Double=0, Optional Safe2 As Double=0, Optional Safe3 As Double=0)
	Initial value problem of ordinary differential equations (extrapolation method (GBS algorithm)) (Reverse communication version)
Sub	Retarda (N As Long, F As LongPtr, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Grid() As Double, Cont() As Double, ICont() As Long, Info As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Nstiff As Long=0, Optional Ngrid As Long=0, Optional Mxst As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0, Optional Beta As Double=0)
	Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method)
Sub	Retarda_r (N As Long, T As Double, Y() As Double, Tout As Double, Tend As Double, RTol() As Double, ATol() As Double, Mode As Long, Grid() As Double, Cont() As Double, ICont() As Long, Info As Long, TT As Double, YY() As Double, YYp() As Double, IRev As Long, Optional Neval As Long, Optional Nstep As Long, Optional Naccept As Long, Optional Nreject As Long, Optional MaxIter As Long=0, Optional Nstiff As Long=0, Optional Ngrid As Long=0, Optional Mxst As Long=0, Optional Cnt As Long=0, Optional Hinit As Double=0, Optional Hmax As Double=0, Optional Fac1 As Double=0, Optional Fac2 As Double=0, Optional Safe As Double=0, Optional Beta As Double=0)
	Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (Reverse communication version)
Sub	Ylaga (I As Long, N As Long, T As Double, Y() As Double, Phi As LongPtr, Cont() As Double, ICont() As Long, Optional Info As Long)
	Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (Computation of back-values of solution)

Detailed Description

This is the group of I1a1. Initial value problem of ordinary differential equations (for non-stiff problem).