XLPack 7.0
XLPack Numerical Library (C API) Reference Manual
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derkf
derkf_int
derkf_r
dop853
dop853_r
dopri5
dopri5_r
doprin
doprin_r
dverk
dverk_int
dverk_r
odex
odex2
odex2_r
odex_r
retard
retard_r

◆ doprin_r()

void doprin_r ( int  n,
double *  t,
double  y[],
double  yp[],
double  tout,
double *  rtol,
double *  atol,
int  itol,
int  iout,
double  work[],
int  lwork,
int  iwork[],
int  liwork,
int *  info,
double *  tt,
double  yy[],
double  yypp[],
int *  irtrn,
int *  irev 
)

Initial value problem of ordinary differential equations (7(6)-th order Runge-Kutta-Nystrom method) (for second order differential equations) (reverse communication version)

NOTE - THIS ROUTINE IS DEPRECATED AND WILL BE REMOVED IN THE NEXT VERSION.

Purpose
This routine integrates a system of second order ordinary differential equations of the form
d2y/dt2 = f(t, y), y = y0, y' = y'0 at t = t0
where t0, y0 and y'0 are the given initial values of t, y and y', respectively. y and y' may be a vector if the above is a system of differential equations.

This routine is the code of the Runge-Kutta-Nystrom method of order 7(6) by Dormand and Prince with step size control.

See for details in the reference below.

doprin_r is the reverse communication version of doprin.
Parameters
[in]nNumber of differential equations. (n >= 1)
[in,out]tThis routine integrates from t to tout. The initial point of the integration is to be given, and the last point of the final step will be returned.
[in] Initial value of the independent variable t.
[out] Last value of the independent variable t of the final step (normally equals to tout). The solution was successfully advanced to this point. It is possible to continue the integration to new point by recalling this routine with the new tout value.
[in,out]y[]Array y[ly] (ly >= n)
[in] Initial values of the dependent variables y[] at initial t.
[out] Computed solution approximation at last t (normally equals to tout).
[in,out]yp[]Array yp[lyp] (lyp >= n)
[in] Initial derivative values y'1, ..., y'n at initial t.
[out] Computed approximations of derivatives at last t (normally euqals to tout).
[in]toutSet tout to the point at which a solution is desired. Integration either forward in t (tout > t) or backward in t (tout < t) is permitted.
The routine advances the solution from t to tout using step sizes which are automatically selected so as to achieve the desired accuracy.
[in]rtolScalar if itol = 0, or array rtol[lrtol] if itol = 1 (lrtol >= n) (rtol or all components of rtol[] >= 0)
The relative error tolerance(s). The routine keeps, roughly, the local error of y[i] below
  rtol*abs(y[i]) + atol (i = 0 to n-1) (if itol = 0)
    or
  rtol[i]*abs(y[i]) + atol[i] (i = 0 to n-1) (if itol = 1).
Both rtol and atol, or, rtol[i] and atol[i] (i = 0 to n-1) should not be 0 at the same time.
[in]atolScalar if itol = 0, or array atol[latol] if itol = 1 (latol >= n) (atol or all components of atol[] >= 0)
The absolute error tolerance(s). The routine keeps, roughly, the local error of y[i] below
  rtol*abs(y[i]) + atol (i = 0 to n-1) (if itol = 0)
    or
  rtol[i]*abs(y[i]) + atol[i] (i = 0 to n-1) (if itol = 1).
Both rtol and atol, or, rtol[i] and atol[i] (i = 0 to n-1) should not be 0 at the same time.
[in]itolSpecifies whether the parameters rtol and atol are scalars or arrays.
= 0: rtol and atol are scalars.
= 1: rtol and atol are arrays.
(For other values, itol = 0 is assumed.)
[in]ioutSwitch to return to print out the intermediate solutions (see irev = 50, 51).
= 0: Not return
= 1: Return for intermediate output
(For other values, iout = 0 is assumed.)
[in,out]work[]Array work[lwork]
Work array.
work[0] to work[19] serve as parameters for the program. If the input parameter is set to 0, the default parameter value defined for each parameter will be loaded.
[in]
work[0]: Initial step size (default = estimated by the code)
work[1]: Maximum step size (default = tout - t)
work[3] and work[4]: Parameters for step size selection. The new step size is chosen subject to the restriction work[3] <= hnew/hold <= work[4]. (default work[3] = 0.2, work[4] = 10)
work[7]: The safety factor in step size prediction (0.0001 < work[7] < 1). If work[7] <= 0.0001 or work[7] >= 1, default value is used. (default = 0.9)
[out]
work[0]: Last step size
[in]lworkSize of array work[]. (lwork >= 6*n + 20)
If lwork < 0, abs(lwork) will be used and work[0] to work[19] will be initialized to zeros.
[in,out]iwork[]Array iwork[liwork]
Work array.
iwork[0] to iwork[19] serve as parameters for the program. If the input parameter is set to 0, the default parameter value defined for each parameter will be loaded.
[in]
iwork[1]: Maximum number of allowed steps. (default = 10000) (if iwork[1] < 0, default value will be used)
iwork[12]: Specifies when iwork[13] to iwork[17] are reset to zero.
= 0: Reset whenever this routine is called.
!= 0: Reset if info = 0.
[out]
iwork[13]: nfcn = number of function evaluations
iwork[15]: nstep = number of computed steps
iwork[16]: naccept = number of accepted steps
iwork[17]: nreject = number of rejected steps (due to error test)
[in]liworkSize of array iwork[]. (liwork >= 20)
If liwork < 0, abs(liwork) will be used and iwork[0] to iwork[19] will be initialized to zeros.
[in,out]info[in]
= 0: Initialize and start computation (Solve new problem).
= 1: Continue computation with new tout value (Resume computation of previous call).
[out]
= -1: The argument n had an illegal value. (n < 1)
= -6: The argument rtol had an illegal value (rtol < 0 or rtol[i] < 0)
= -6: The argument rtol or atol had an illegal value (rtol = 0 and atol = 0, or rtol[i] = 0 and atol[i] = 0)
= -7: The argument atol had an illegal value (atol < 0 or atol[i] < 0)
= -11: The argument lwork had an illegal value (lwork too small)
= -13: The argument liwork had an illegal value (liwork too small)
= -14: the argument info had an illegal value (info != 0 nor 1)
= -19: the argument irev had an illegal value (irev != 1, ..., 10, 50 nor 51)
= 1: Successful exit
= 2: Interrupted by irtrn (normal return)
= 11: Convergence failure (maximum number of steps exceeded, etc.).
[out]ttirev = 1 to 10: The value of t where the second derivative values should be evaluated and given in yypp[] in the next call.
irev = 50 or 51: The current value of t.
[out]yy[]Array yy[lyy] (lyy >= n)
irev = 1 to 10: The value of y where the second derivative values should be evaluated and given in yypp[] in the next call.
irev = 50 or 51: The value of y at current t.
[in,out]yypp[]Array yypp[lyypp] (lyypp >= n)
[in] irev = 1 to 10: The computed second derivatives at given t (= tt) and y (= yy[]), i.e. yypp[i] = d2yi/dt2 = fi(tt, yy[0], ..., yy[n-1]) (i = 0 to n-1), should be given in the next call.
[out] irev = 50 or 51: The value of yp at current t.
[in,out]irtrn[in] irev = 50 or 51: Do not alter irtrn unless user want to interrupt the integration. If irtrn is set to the negative value, the integration will be interrupted and exit with info = 2. [out] irev = 50 or 51: The output value will be 0, 1 or 2 in the first, intermediate or last return with irev = 50 or 51, respectively.
[in,out]irevControl variable for reverse communication.
[in] Before first call, irev should be initialized to zero. On succeeding calls, irev should not be altered.
[out] If irev is not zero, complete the following process and call this routine again.
= 0: Computation finished. See return code in info.
= 1 to 10: User should set the computed second derivative values at tt and yy[] in yypp[]. Do not alter any variables other than yypp[].
= 50, 51: To be returned with this code to print out the intermediate solutions after every successful step if iout = 1. The values t, y and yp are provided in tt, yy[] and yypp[].
Reference
  • E. Hairer, S.P. Norsett and G. Wanner, "Solving Ordinary Differential Equations I", Springer Series in Computational Mathematics, Springer-Verlag (1987)
  • J. R. Dormand and P. J. Prince, "New Runge-Kutta algorithms for numerical simulation in dynamical astoronomy", Celestial Mechanics 18, 223?232 (1978)
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