NAG Library Routine Document

D02XKF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     XSOL – REAL (KIND=nag_wp)Input

On entry: the point at which the first $m$ components of the solution are to be evaluated. XSOL should not be an extrapolation point, that is XSOL should satisfy $\left(\mathbf{XSOL}-\mathbf{X}\right)\times \mathbf{HU}\le 0.0$. Extrapolation is permitted but not recommended.

2:     SOL(M) – REAL (KIND=nag_wp) arrayOutput

On exit: the calculated value of the $\mathit{i}$th component of the solution at XSOL, for $\mathit{i}=1,2,\dots ,m$.

3:     M – INTEGERInput

On entry: the number of components of the solution whose values at XSOL are required. The first $m$ components are evaluated.

Constraint: $1\le \mathbf{M}\le \mathbf{NEQ}$.

4:     YSAV(LDYSAV,SDYSAV) – REAL (KIND=nag_wp) arrayInput

On entry: the values provided in the parameter YSAV on return from the integrator.

5:     LDYSAV – INTEGERInput

On entry: the value used for the parameter LDYSAV when calling the integrator.

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

6:     SDYSAV – INTEGERInput

On entry: the value used for the parameter SDYSAV when calling the integrator.

Constraint: $\mathbf{SDYSAV}\ge \mathbf{NQU}+1$.

7:     ACOR(NEQ) – REAL (KIND=nag_wp) arrayInput

On entry: the value returned in position $\left(\mathbf{LDYSAV}+50+\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NEQ}$, of the parameter RWORK returned by the integrator. If one of the forward communication D02N routines is being employed and D02XKF is to be used in MONITR, then $\mathbf{ACOR}\left(\mathit{i}\right)$ must contain the value given in position $\left(\mathit{i},2\right)$ of the MONITR parameter ACOR, for $\mathit{i}=1,2,\dots ,\mathbf{NEQ}$ (e.g., see D02NBF).

8:     NEQ – INTEGERInput

On entry: the value used for the parameter NEQ when calling the integrator.

Constraint: $1\le \mathbf{NEQ}\le \mathbf{LDYSAV}$.

9:     X – REAL (KIND=nag_wp)Input

On entry: the latest value at which the solution has been computed, as provided in the parameter TCUR on return from the optional output D02NYF.

10:   NQU – INTEGERInput

On entry: the order of the method used up to the latest value at which the solution has been computed, as provided in the parameter NQU on return from the optional output D02NYF.

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

11:   HU – REAL (KIND=nag_wp)Input

On entry: the last successful step used, that is the step used in the integration to get to X, as provided in the parameter HU on return from the optional output D02NYF.

12:   H – REAL (KIND=nag_wp)Input

On entry: the next step size to be attempted in the integration, as provided in the parameter H on return from the optional output D02NYF.

13:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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).

If D02XKF is to be used for extrapolation, IFAIL must be set to $1$ before entry. It is then essential to test the value of IFAIL on exit for $\mathbf{IFAIL}=\mathbf{1}$ or $\mathbf{2}$.

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{M}<1$,
or	$\mathbf{NEQ}<1$,
or	$\mathbf{LDYSAV}<1$,
or	$\mathbf{NEQ}>\mathbf{LDYSAV}$,
or	$\mathbf{M}>\mathbf{NEQ}$,
or	$\mathbf{NQU}<1$,
or	$\mathbf{SDYSAV}<\mathbf{NQU}+1$,
or	the BDF integrator was not previously used,
or	the Petzold error test, if applicable, was used.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{HU}=0.0$ or $\mathbf{H}=0.0$. This error can only occur if H and HU have been changed by you or possibly if the integrator has failed before calling D02XKF.

$\mathbf{IFAIL}=3$

D02XKF has been called for extrapolation. Before returning with this error exit, the value of the solution at XSOL is calculated and placed in SOL.

7  Accuracy

8  Further Comments

9  Example