NAG Library Routine Document

D02MVF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

D02MVF is an integration method specific setup routine which must be called prior to linear algebra setup routines and integrators from the SPRINT suite of routines, if the DASSL implementation of Backward Differentiation Formulae (BDF) is to be used. Note that this method is also available, independent from the SPRINT suite, using D02NEF

2 Specification

SUBROUTINE D02MVF (	NEQMAX, SDYSAV, MAXORD, CON, TCRIT, HMIN, HMAX, H0, MAXSTP, MXHNIL, NORM, RWORK, IFAIL)
INTEGER	NEQMAX, SDYSAV, MAXORD, MAXSTP, MXHNIL, IFAIL
*double precision*	CON(3), TCRIT, HMIN, HMAX, H0, RWORK(50+4*NEQMAX)
CHARACTER*1	NORM

3 Description

An integrator setup routine must be called before the call to any linear algebra setup routine or integrator from the SPRINT suite of routines in this sub-chapter. This setup routine, D02MVF, makes the choice of the DASSL integrator and permits you to define options appropriate to this choice. Alternative choices of integrator from this suite are the BDF method and the BLEND method which can be chosen by initial calls to D02NVF or D02NWF respectively.

4 References

See the D02M–N sub-chapter Introduction.

5 Parameters

1: NEQMAX – INTEGERInput

On entry: a bound on the maximum number of differential equations to be solved.

Constraint: NEQMAX≥1.

2: SDYSAV – INTEGERInput

On entry: the second dimension of the array YSAV that will be supplied to the integrator, as declared in the (sub)program from which the integrator is called (e.g., see D02NBF).

Constraint: SDYSAV≥MAXORD+3.

3: MAXORD – INTEGERInput

On entry: the maximum order to be used for the BDF method. If MAXORD=0 then MAXORD=5 is assumed.

Constraint: 0≤MAXORD≤5.

4: CON(3) – double precision arrayInput/Output

On entry: values to be used to control step size choice during integration. If any CONi=0.0 on entry, it is replaced by its default value described below. In most cases this is the recommended setting.

CON1, CON2, and CON3 are factors used to bound step size changes. If the current step size h fails, then the modulus of the next step size is bounded by CONl×h. The default value of CON1 is 2.0. Note that the new step size may be used with a method of different order to the failed step. If the initial step size is h, then the modulus of the step size on the second step is bounded by CON3×h. At any other stage in the integration, if the current step size is h, then the modulus of the next step size is bounded by CON2×h. The default values are 10.0 for CON2 and 1000.0 for CON3.

Constraints:

These constraints must be satisfied after any zero values have been replaced by default values.

0.0<CON1<CON2<CON3;
CON2>1.0;
CON3>1.0.

On exit: the values actually to be used by the integration routine.

5: TCRIT – double precisionInput

On entry: a point beyond which integration must not be attempted. The use of TCRIT is described under the parameter ITASK in the specification for the integrator (e.g., see D02NBF). A value, 0.0 say, must be specified even if ITASK subsequently specifies that TCRIT will not be used.

6: HMIN – double precisionInput

On entry: the minimum absolute step size to be allowed. Set HMIN=0.0 if this option is not required.

7: HMAX – double precisionInput

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

8: H0 – double precisionInput

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

9: MAXSTP – INTEGERInput

On entry: the maximum number of steps to be attempted during one call to the integrator after which it will return with IFAIL=2 (e.g., see D02NBF). Set MAXSTP=0 if no limit is to be imposed.

10: MXHNIL – INTEGERInput

On entry: the maximum number of warnings printed (if ITRACE≥0, e.g., see D02NBF) per problem when t+h=t on a step (h= current step size). If MXHNIL≤0, a default value of 10 is assumed.

11: NORM – CHARACTER*1Input

On entry: indicates the type of norm to be used.

NORM='M': Maximum norm.
NORM='A': Averaged L2 norm.
NORM='D': Is the same as 'A'.

If vnorm denotes the norm of the vector v of length n, then for the averaged L2 norm

vnormB=1n∑i=1n viwi 2,

while for the maximum norm

vnorm=max1≤i≤n viwi .

If you wish to weight the maximum norm or the L2 norm, then RTOL and ATOL should be scaled appropriately on input to the integrator (see under ITOL in the specification of the integrator for the formulation of the weight vector wi from RTOL and ATOL, e.g., see D02NBF).

Only the first character to the actual parameter NORM is passed to D02MVF; hence it is permissible for the actual argument to be more descriptive, e.g., ‘Maximum’, ‘Average L2’ or ‘Default’ in a call to D02MVF.

Constraint: NORM='M', 'A' or 'D'.

12: RWORK(50+4×NEQMAX) – double precision arrayCommunication Array

This must be the same workspace array as the array RWORK supplied to the integrator. It is used to pass information from the setup routine to the integrator and therefore the contents of this array must not be changed before calling the integrator.

13: IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to 0, -1 or 1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

On exit: IFAIL=0 unless the routine detects an error (see Section 6).

For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 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 -1 or 1 is used it is essential to test the value of IFAIL on exit.