NAG Library Routine Document

d02phf  (ivp_rk_interp_setup)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{irevcm}$ – IntegerInput/Output

On initial entry: irevcm must be set to zero to indicate that the interpolant for a new step is being taken.

On intermediate re-entry: irevcm should remain unchanged.

On intermediate exit: irevcm returns a value $1$ to indicate that a function evaluation is required prior to re-entry; the value of the derivatives must be returned in yp where the value of $t$ is supplied in t and the values $y\left(t\right)$ are supplied in the array y.

On final exit:

$\mathbf{irevcm}=-1$

Successful exit; rwsav and wcomm contain details of the interpolant.

$\mathbf{irevcm}=-2$

Error exit; ifail should be interrogated to determine the nature of the error.

Note: any values you return to d02phf as part of the reverse communication procedure should not include floating-point NaN (Not a Number) or infinity values, since these are not handled by d02phf. If your code inadvertently does return any NaNs or infinities, d02phf is likely to produce unexpected results.

2:     $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 1$. This must be the same value as supplied in a previous call to d02pqf.

3:     $\mathbf{nwant}$ – IntegerInput

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

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

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

On intermediate exit: t contains the value of the independent variable $t$ at which the derivatives $y^{\prime }$ are to be evaluated.

On final exit: contains no useful information.

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

On intermediate exit: y contains the value of the solution $y$ at which the derivatives $y^{\prime }$ are to be evaluated.

On final exit: contains no useful information.

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

On initial entry: need not be set.

On intermediate re-entry: yp must contain the values of the derivatives $y_i^{\prime }$ for the given values of the parameters $t$, $y_i$.

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

On entry: wcomm need not be set.

On intermediate re-entry: wcomm contains the partial computation of the polynomial coefficients corresponding to a continuous Runge–Kutta process for interpolating medium and high order Runge–Kutta methods.

On final exit: if $\mathbf{method}=2$, $-2$, $3$ or $-3$, wcomm contains details of the interpolant which must be passed unchanged to d02pjf for evaluation of the interpolant.

8:     $\mathbf{lwcomm}$ – IntegerInput

On entry: length of wcomm.

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 $-3$, lwcomm must be at least $8\times \mathbf{nwant}$.

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, d02pjf or other associated routines.

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

On initial 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, because for this routine the values of the output arguments may be useful even if $\mathbf{ifail}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of ifail on exit.

On final 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, $\mathbf{lwcomm}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$ 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, $\mathbf{nwant}=〈\mathit{\text{value}}〉$ 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 after the range integrator has been called.

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

$\mathbf{ifail}=-99$

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

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Example