d02mwf is a setup routine which must be called prior to the integrator d02nef, if the DASSL implementation of Backward Differentiation Formulae (BDF) is to be used.

2 Specification

Fortran Interface

Subroutine d02mwf (

neq, maxord, jceval, hmax, h0, itol, icom, licom, com, lcom, ifail)

Integer, Intent (In)	::	neq, maxord, itol, licom, lcom
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	icom(licom)
Real (Kind=nag_wp), Intent (In)	::	hmax, h0
Real (Kind=nag_wp), Intent (Out)	::	com(lcom)
Character (1), Intent (In)	::	jceval

C Header Interface

#include <nag.h>

void	d02mwf_ (const Integer neq, const Integer maxord, const char jceval, const double hmax, const double h0, const Integer itol, Integer icom[], const Integer licom, double com[], const Integer lcom, Integer *ifail, const Charlen length_jceval)

The routine may be called by the names d02mwf or nagf_ode_dae_dassl_setup.

3 Description

This integrator setup routine must be called before the first call to the integrator d02nef. This setup routine d02mwf permits you to define options for the DASSL integrator, such as: whether the Jacobian is to be provided or is to be approximated numerically by the integrator; the initial and maximum step-sizes for the integration; whether relative and absolute tolerances are system wide or per system equation; and the maximum order of BDF method permitted.

4 References

None.

5 Arguments

1: $neq$ – Integer Input

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

Constraint:

neq \geq 1

2: $maxord$ – Integer Input

On entry: the maximum order to be used for the BDF method. Orders up to 5th order are available; setting

maxord > 5

means that the maximum order used will be

5

Constraint:

1 \leq maxord

3: $jceval$ – Character(1) Input

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

$jceval ='N'$: The Jacobian is to be evaluated numerically by the integrator.
$jceval ='A'$: 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:

jceval ='N'

'A'

4: $hmax$ – Real (Kind=nag_wp) Input

On entry: the maximum absolute step size to be allowed. Set

hmax = 0.0

if this option is not required.

Constraint:

hmax \geq 0.0

5: $h0$ – Real (Kind=nag_wp) Input

On entry: the step size to be attempted on the first step. Set

h0 = 0.0

if the initial step size is calculated internally.

6: $itol$ – Integer Input

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

$itol = 0$: rtol and atol are single element vectors.
$itol = 1$: 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:

itol = 0

1

7: $icom (licom)$ – Integer array Communication Array

On exit: used to communicate details of the task to be carried out to the integration routine d02nef.

8: $licom$ – Integer Input

On entry: the dimension of the array icom as declared in the (sub)program from which d02mwf is called.

Constraint:

licom \geq neq + 50

9: $com (lcom)$ – Real (Kind=nag_wp) array Communication 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: $lcom$ – Integer Input

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, $lcom \geq 40 + (maxord + 4) \times neq + {neq}^{2}$ ;
if the system Jacobian is banded, $lcom \geq 40 + (maxord + 4) \times neq + (2 \times ml + mu + 1) \times neq + 2 \times (neq / (ml + mu + 1) + 1)$ .

Here ml and mu are the lower and upper bandwidths respectively that are to be specified in a subsequent call to d02npf.

11: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

−1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

−1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $neq = ⟨ value ⟩$ .
Constraint: $neq \geq 1$ .

$ifail = 2$: On entry, $maxord = ⟨ value ⟩$ .
Constraint: $maxord \geq 1$ .

$ifail = 3$: On entry, jceval has an illegal value: $jceval = ⟨ value ⟩$ .
Constraint: $jceval ='N'$ or $'A'$ .

$ifail = 4$: On entry, $hmax = ⟨ value ⟩$ .
Constraint: $hmax \geq 0.0$ .

$ifail = 6$: On entry, $itol = ⟨ value ⟩$ .
Constraint: $itol = 0$ or $1$ .

$ifail = 8$: On entry, $licom = ⟨ value ⟩$ and $neq = ⟨ value ⟩$ .
Constraint: $licom \geq 50 + neq$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

d02mwf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example solves the plane pendulum problem, defined by the following equations:

\begin{matrix} x^{'} & = & u \\ y^{'} & = & v \\ u^{'} & = & - λ x \\ v^{'} & = & - λ y - 1 \\ x^{2} + y^{2} & = & 1 . \end{matrix}

Differentiating the algebraic constraint once, a new algebraic constraint is obtained

x u + y v = 0 .

Differentiating the algebraic constraint one more time, substituting for

x^{'}

y^{'}

u^{'}

v^{'}

and using

x^{2} + y^{2} - 1 = 0

, the corresponding DAE system includes the differential equations and the algebraic equation in

λ

u^{2} + v^{2} - λ - y = 0 .

We solve the reformulated DAE system

\begin{matrix} y_{1}^{'} & = & y_{3} \\ y_{2}^{'} & = & y_{4} \\ y_{3}^{'} & = & - y_{5} \times y_{1} \\ y_{4}^{'} & = & - y_{5} \times y_{2} - 1 \\ y_{3}^{2} + y_{4}^{2} - y_{5} - y_{2} & = & 0 . \end{matrix}

For our experiments, we take consistent initial values

y_{1} (0) = 1, ​ y_{2} (0) = 0, ​ y_{3} (0) = 0, ​ y_{4} (0) = 1 ​ and ​ y_{5} (0) = 1

t = 0

d02mw: FL CL CPP AD PY MB

NAG FL Interfaced02mwf (dae_​dassl_​setup)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
d02mwf (dae_dassl_setup)