NAG Library Routine Document

d02pjf (ivp_rk_interp_eval)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{icheck}$ – IntegerInput

On entry: indicates whether consistency checks on input arguments should be performed

$\mathbf{icheck}\ne 1$

Don't perform checks on input arguments.

$\mathbf{icheck}=1$

Perform consistency checks on input arguments.

It is recommended to use $\mathbf{icheck}=1$ on the first call following a call to d02phf and to set $\mathbf{icheck}\ne 1$ on subsequent calls within the last step to avoid the overhead of argument checking.

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the dimension of the system of ODEs being integrated.

Constraint: this must be the same value as supplied in a previous call to d02pqf.

3:     $\mathbf{nwant}$ – IntegerInput

On entry: only the first nwant system components to be computed. This should be the same value as passed to d02phf when computing the interpolant.

Constraint: $\mathbf{nwant}=\mathbf{nwant}$ passed to d02phf.

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

On entry: $t$, the value of the independent variable where a solution is desired. Although any value of $t$ can be supplied, accurate solutions can only be obtained for values in the range of the last time-step taken by d02pgf.

5:     $\mathbf{ideriv}$ – IntegerInput

On entry:

$\mathbf{ideriv}=0$

Compute approximations to the first nwant components of the solution $y\left(t\right)$.

$\mathbf{ideriv}=1$

Compute approximations to the first nwant components of the first derivatives of the solution $y^{\prime }\left(t\right)$.

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

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

On exit:

$\mathbf{ideriv}=0$

The first nwant components of the solution $y\left(t\right)$.

$\mathbf{ideriv}=1$

The first nwant components of the first derivatives of the solution $y^{\prime }\left(t\right)$.

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

On entry: this must be the same array supplied in a previous call to d02phf. It must remain unchanged between calls.

8:     $\mathbf{lwcomm}$ – IntegerInput

On entry: length of wcomm. This should be the same value as supplied in a previous call to d02phf.

If in a previous call to d02pqf:

• $\mathbf{method}=1$ or $-1$, lwcomm must be at least $1$.
• $\mathbf{method}=2$ or $-2$, lwcomm must be at least $\mathbf{n}+\max \left(\mathbf{n},5\times \mathbf{nwant}\right)$.
• $\mathbf{method}=3$ or $-3$, $\mathbf{lwcomm}\ge 8\times \mathbf{nwant}$.

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

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

On entry: these must be the same arrays supplied in a previous call d02pgf. They must remain unchanged between calls.

On exit: information about the integration for use on subsequent calls to d02pgf, d02phf or other associated routines.

11:   $\mathbf{ifail}$ – 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

$\mathbf{ifail}=1$

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: $\mathbf{ideriv}=0$ or $1$.

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, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$ and $\mathbf{nwant}=〈\mathit{\text{value}}〉$.
Constraint: for $\mathbf{method}=-3$ or $3$, $\mathbf{lwcomm}\ge 8\times \mathbf{nwant}$.

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

On entry, $\mathbf{nwant}=〈\mathit{\text{value}}〉$, but on interpolation setup $\mathbf{nwant}=〈\mathit{\text{value}}〉$.
Constraint: nwant must be unchanged from setup.

The previous call to the interpolation setup routine returned an error.

You cannot call this routine before you have called the interpolation setup.

$\mathbf{ifail}=-99$

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