NAG Library Routine Document

D02NYF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NEQ – INTEGERInput

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

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

2:     NEQMAX – INTEGERInput

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

Constraint: $\mathbf{NEQMAX}\ge \mathbf{NEQ}$.

3:     HU – REAL (KIND=nag_wp)Output

On exit: the last successful step size.

4:     H – REAL (KIND=nag_wp)Output

On exit: the proposed next step size for continuing the integration.

5:     TCUR – REAL (KIND=nag_wp)Output

On exit: $t$, the value of the independent variable which the integrator has actually reached. TCUR will always be at least as far as the output value of the argument $t$ in the direction of integration, but may be further (if overshooting and interpolation at TOUT was specified, e.g., see D02NBF).

6:     TOLSF – REAL (KIND=nag_wp)Output

On exit: a tolerance scale factor, $\mathbf{TOLSF}\ge 1.0$, which is computed when a request for too much accuracy is detected by the integrator (indicated by a return with $\mathbf{IFAIL}=\mathbf{3}$ or $\mathbf{14}$). If ITOL is left unaltered but RTOL and ATOL are uniformly scaled up by a factor of TOLSF the next call to the integrator is deemed likely to succeed.

7:     RWORK($50+4\times \mathbf{NEQ}$) – REAL (KIND=nag_wp) arrayCommunication Array

On entry: contains information supplied by the integrator.

8:     NST – INTEGEROutput

On exit: the number of steps taken in the integration so far.

9:     NRE – INTEGEROutput

On exit: the number of function or residual evaluations (FCN (e.g., see D02NBF) or RESID (e.g., see D02NGF) calls) used in the integration so far.

10:   NJE – INTEGEROutput

On exit: the number of Jacobian evaluations used in the integration so far. This equals the number of matrix $LU$ decompositions.

11:   NQU – INTEGEROutput

On exit: the order of the method last used (successfully) in the integration.

12:   NQ – INTEGEROutput

On exit: the proposed order of the method for continuing the integration.

13:   NITER – INTEGEROutput

On exit: the number of iterations performed in the integration so far by the nonlinear equation solver.

14:   IMXER – INTEGEROutput

On exit: the index of the component of largest magnitude in the weighted local error vector $\left(e_{\mathit{i}}/w_{\mathit{i}}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NEQ}$.

15:   ALGEQU(NEQ) – LOGICAL arrayOutput

On exit: $\mathbf{ALGEQU}\left(\mathit{i}\right)=\mathrm{.TRUE.}$ if the $\mathit{i}$th equation integrated was detected to be algebraic, otherwise $\mathbf{ALGEQU}\left(\mathit{i}\right)=\mathrm{.FALSE.}$. Note that when the integrators for explicit equations are being used, then $\mathbf{ALGEQU}\left(\mathit{i}\right)=\mathrm{.FALSE.}$, for $\mathit{i}=1,2,\dots ,\mathbf{NEQ}$.

16:   INFORM($23$) – INTEGER arrayCommunication Array

On entry: contains information supplied by the integrator.

17:   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).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{NEQ}<1$,
or	$\mathbf{NEQMAX}<1$,
or	$\mathbf{NEQ}>\mathbf{NEQMAX}$.

7  Accuracy

8  Further Comments

9  Example