NAG Library Routine Document

d02psf  (ivp_rkts_interp)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of ordinary differential equations in the system to be solved by the integration routine.

Constraint: $\mathbf{n}\ge 1$.

2:     $\mathbf{twant}$ – Real (Kind=nag_wp)Input

On entry: $t$, the value of the independent variable where a solution is desired.

3:     $\mathbf{ideriv}$ – IntegerInput

On entry: determines whether the solution and/or its first derivative are to be computed

$\mathbf{ideriv}=0$

compute approximate solution.

$\mathbf{ideriv}=1$

compute approximate first derivative.

$\mathbf{ideriv}=2$

compute approximate solution and first derivative.

Constraint: $\mathbf{ideriv}=0$, $1$ or $2$.

4:     $\mathbf{nwant}$ – IntegerInput

On entry: the number of components of the solution to be computed. The first nwant components are evaluated.

Constraint: $1\le \mathbf{nwant}\le \mathbf{n}$.

5:     $\mathbf{ywant}\left(\mathbf{nwant}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: an approximation to the first nwant components of the solution at twant if $\mathbf{ideriv}=0$ or $2$. Otherwise ywant is not defined.

6:     $\mathbf{ypwant}\left(\mathbf{nwant}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: an approximation to the first nwant components of the first derivative at twant if $\mathbf{ideriv}=1$ or $2$. Otherwise ypwant is not defined.

7:     $\mathbf{f}$ – Subroutine, supplied by the user.External Procedure

f must evaluate the functions $f_i$ (that is the first derivatives $y_i^{\prime }$) for given values of the arguments $t,y_i$. It must be the same procedure as supplied to d02pff.

The specification of f is:

Fortran Interface

Subroutine f ( t, n, y, yp, iuser, ruser) Integer, Intent (In) :: n Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: t, y(n) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (Out) :: yp(n)

C Header Interface

#include nagmk26.h void  f ( const double *t, const Integer *n, const double y[], double yp[], Integer iuser[], double ruser[])

1:     $\mathbf{t}$ – Real (Kind=nag_wp)Input

On entry: $t$, the current value of the independent variable.

2:     $\mathbf{n}$ – IntegerInput

On entry: $\mathit{n}$, the number of ordinary differential equations in the system to be solved.

3:     $\mathbf{y}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the current values of the dependent variables, $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,\mathit{n}$.

4:     $\mathbf{yp}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the values of $f_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,\mathit{n}$.

5:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

6:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

f is called with the arguments iuser and ruser as supplied to d02psf. You should use the arrays iuser and ruser to supply information to f.

f must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d02psf is called. Arguments denoted as Input must not be changed by this procedure.

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by d02psf. If your code inadvertently does return any NaNs or infinities, d02psf is likely to produce unexpected results.

8:     $\mathbf{wcomm}\left(\mathbf{lwcomm}\right)$ – Real (Kind=nag_wp) arrayCommunication Array

On entry: this array stores information that can be utilized on subsequent calls to d02psf.

9:     $\mathbf{lwcomm}$ – IntegerInput

On entry: length of wcomm.

If in a previous call to d02pqf:

• $\mathbf{method}=1$ or $-1$ then lwcomm must be at least $1$.
• $\mathbf{method}=2$ or $-2$ then lwcomm must be at least $\mathbf{n}+\max \left(\mathbf{n},5\times \mathbf{nwant}\right)$.
• $\mathbf{method}=3$ or $-3$ then wcomm and lwcomm are not referenced.

10:   $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

11:   $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

iuser and ruser are not used by d02psf, but are passed directly to f and may be used to pass information to this routine.

12:   $\mathbf{iwsav}\left(130\right)$ – Integer arrayCommunication Array

13:   $\mathbf{rwsav}\left(32\times \mathbf{n}+350\right)$ – Real (Kind=nag_wp) arrayCommunication Array

On entry: these must be the same arrays supplied in a previous call d02pff. They must remain unchanged between calls.

On exit: information about the integration for use on subsequent calls to d02pff, d02psf or other associated routines.

14:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

$\mathbf{method}=-3$ or $3$ in setup, but interpolation is not available for this method. Either use $\mathbf{method}=-2$ or $2$ in setup or use reset routine to force the integrator to step to particular points.

On entry, a previous call to the setup routine has not been made or the communication arrays have become corrupted, or a catastrophic error has already been detected elsewhere.
You cannot continue integrating the problem.

On entry, $\mathbf{ideriv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ideriv}=0$, $1$ or $2$.

On entry, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{nwant}=〈\mathit{\text{value}}〉$.
Constraint: for $\mathbf{method}=-2$ or $2$, $\mathbf{lwcomm}\ge \mathbf{n}+\max \left(\mathbf{n},5\times \mathbf{nwant}\right)$.

On entry, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$.
Constraint: for $\mathbf{method}=-1$ or $1$, $\mathbf{lwcomm}\ge 1$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$, but the value passed to the setup routine was $\mathbf{n}=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{nwant}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{nwant}\le \mathbf{n}$.

You cannot call this routine after the integrator has returned an error.

You cannot call this routine before you have called the step integrator.

You cannot call this routine when you have specified, in the setup routine, that the range integrator will be used.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d02psfe.f90)

10.2

Program Data

Program Data (d02psfe.d)

10.3

Program Results

Program Results (d02psfe.r)