NAG Library Routine Document

d02xjf (ivp_stiff_nat_interp)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{xsol}$ – 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:     $\mathbf{sol}\left(\mathbf{m}\right)$ – 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:     $\mathbf{m}$ – IntegerInput

On entry: $m$, 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:     $\mathbf{ysav}\left(\mathbf{ldysav},\mathbf{sdysav}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the values provided in the argument ysav on return from the integrator.

5:     $\mathbf{ldysav}$ – IntegerInput

On entry: the value used for the argument ldysav when calling the integrator.

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

6:     $\mathbf{sdysav}$ – IntegerInput

On entry: the value used for the argument sdysav when calling the integrator.

Constraint: $\mathbf{sdysav}\ge \mathbf{nqu}+1$.

7:     $\mathbf{neq}$ – IntegerInput

On entry: the value used for the argument neq when calling the integrator.

Constraint: $1\le \mathbf{neq}\le \mathbf{ldysav}$.

8:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: the latest value at which the solution has been computed, as provided in the argument tcur on return from the optional output d02nyf.

9:     $\mathbf{nqu}$ – 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 argument nqu on return from the optional output d02nyf.

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

10:   $\mathbf{hu}$ – 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 argument hu on return from the optional output d02nyf.

11:   $\mathbf{h}$ – Real (Kind=nag_wp)Input

On entry: the next step size to be attempted in the integration, as provided in the argument h on return from the optional output d02nyf.

12:   $\mathbf{ifail}$ – 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).

If d02xjf 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, $\mathbf{ldysav}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldysav}\ge 1$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{neq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\le \mathbf{neq}$.

On entry, $\mathbf{neq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{neq}\ge 1$.

On entry, $\mathbf{neq}=〈\mathit{\text{value}}〉$ and $\mathbf{ldysav}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{neq}\le \mathbf{ldysav}$.

On entry, $\mathbf{nqu}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nqu}\ge 1$.

On entry, $\mathbf{sdysav}=〈\mathit{\text{value}}〉$ and $\mathbf{nqu}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{sdysav}\ge \mathbf{nqu}+1$.

$\mathbf{ifail}=2$

On entry, $\mathbf{h}=0.0$.

On entry, $\mathbf{hu}=0.0$.

$\mathbf{ifail}=3$

On entry, $\mathbf{xsol}=〈\mathit{\text{value}}〉$, $\mathbf{x}=〈\mathit{\text{value}}〉$ and $\mathbf{h}=〈\mathit{\text{value}}〉$.
Constraint: xsol should not be an extrapolation point.

$\mathbf{ifail}=-99$

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