NAG Library Routine Document

D02MWF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NEQ – INTEGERInput

On entry: the number of differential-algebraic equations to be solved.

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

2:     MAXORD – INTEGERInput

On entry: the maximum order to be used for the BDF method. Orders up to 5th order are available; setting $\mathbf{MAXORD}>5$ means that the maximum order used will be $5$.

Constraint: $1\le \mathbf{MAXORD}$.

3:     JCEVAL – CHARACTER(1)Input

On entry: specifies the technique to be used to compute the Jacobian.

$\mathbf{JCEVAL}=\text{'N'}$

The Jacobian is to be evaluated numerically by the integrator.

$\mathbf{JCEVAL}=\text{'A'}$

You must supply a subroutine to evaluate the Jacobian on a call to the integrator.

Only the first character of the actual paramater JCEVAL is passed to D02MWF; hence it is permissible for the actual argument to be more descriptive, e.g., ‘Numerical’ or ‘Analytical’, on a call to D02MWF.

Constraint: $\mathbf{JCEVAL}=\text{'N'}$ or $\text{'A'}$.

4:     HMAX – REAL (KIND=nag_wp)Input

On entry: the maximum absolute step size to be allowed. Set $\mathbf{HMAX}=0.0$ if this option is not required.

Constraint: $\mathbf{HMAX}\ge 0.0$.

5:     H0 – REAL (KIND=nag_wp)Input

On entry: the step size to be attempted on the first step. Set $\mathbf{H0}=0.0$ if the initial step size is calculated internally.

6:     ITOL – INTEGERInput

On entry: a value to indicate the form of the local error test.

$\mathbf{ITOL}=0$

RTOL and ATOL are single element vectors.

$\mathbf{ITOL}=1$

RTOL and ATOL are vectors. This should be chosen if you want to apply different tolerances to each equation in the system.

See D02NEF.

Note: the tolerances must either both be single element vectors or both be vectors of length NEQ.

Constraint: $\mathbf{ITOL}=0$ or $1$.

7:     ICOM(LICOM) – INTEGER arrayCommunication Array

On exit: used to communicate details of the task to be carried out to the integration routine D02NEF.

8:     LICOM – INTEGERInput

On entry: the dimension of the array ICOM as declared in the (sub)program from which D02MWF is called.

Constraint: $\mathbf{LICOM}\ge \mathbf{NEQ}+50$.

9:     COM(LCOM) – REAL (KIND=nag_wp) arrayCommunication Array

On exit: used to communicate problem parameters to the integration routine D02NEF. This must be the same communication array as the array COM supplied to D02NEF. In particular, the values of HMAX and H0 are contained in COM.

10:   LCOM – INTEGERInput

On entry: the dimension of the array COM as declared in the (sub)program from which D02MWF is called.

Constraints:

the array COM must be large enough for the requirements of D02NEF. That is:

• if the system Jacobian is dense, $\mathbf{LCOM}\ge 40+\left(\mathbf{MAXORD}+4\right)\times \mathbf{NEQ}+{\mathbf{NEQ}}^2$;
• if the system Jacobian is banded, $$\begin{gathered} \mathbf{LCOM}\ge 40+\left(\mathbf{MAXORD}+4\right)\times \mathbf{NEQ}+\left(2\times \mathbf{ML}+\mathbf{MU}+1\right)\times \mathbf{NEQ}+2\times \\ \left(\mathbf{NEQ}/\left(\mathbf{ML}+\mathbf{MU}+1\right)+1\right) \end{gathered}$$.

Here ML and MU are the lower and upper bandwidths respectively that are to be specified in a subsequent call to D02NPF.

11:   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,

$\mathbf{NEQ}<1$.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{MAXORD}<1$,
or	$\mathbf{MAXORD}>5$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{JCEVAL}\ne \text{'N'}$ or $\text{'A'}$.

$\mathbf{IFAIL}=4$

On entry,

$\mathbf{HMAX}<0.0$.

$\mathbf{IFAIL}=6$

On entry,

$\mathbf{ITOL}\ne 0$ or $1$.

$\mathbf{IFAIL}=8$

On entry,

$\mathbf{LICOM}<\mathbf{NEQ}+50$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (d02mwfe.f90)

9.2  Program Data

Program Data (d02mwfe.d)

9.3  Program Results

Program Results (d02mwfe.r)