d02mwc is a setup function which must be called prior to the integrator d02nec, if the DASSL implementation of Backward Differentiation Formulae (BDF) is to be used.

2 Specification

#include <nag.h>

void	d02mwc (Integer neq, Integer maxord, Nag_EvaluateJacobian jceval, double hmax, double h0, Nag_Boolean vector_tol, Integer icom[], Integer licom, double com[], Integer lcom, NagError *fail)

The function may be called by the names: d02mwc, nag_ode_dae_dassl_setup or nag_dae_ivp_dassl_setup.

3 Description

This integrator setup function must be called before the first call to the integrator d02nec. d02mwc 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: $jceval$ – Nag_EvaluateJacobian Input

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

$jceval = Nag_NumericalJacobian$: The Jacobian is to be evaluated numerically by the integrator.
$jceval = Nag_AnalyticalJacobian$: You must supply a function to evaluate the Jacobian on a call to the integrator.

Constraint:

jceval = Nag_NumericalJacobian

Nag_AnalyticalJacobian

4: $hmax$ – double 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: $h0$ – double 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: $vector_tol$ – Nag_Boolean Input

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

$vector_tol = Nag_FALSE$: rtol and atol are single element vectors.
$vector_tol = Nag_TRUE$: rtol and atol are vectors. This should be chosen if you want to apply different tolerances to each equation in the system.

See d02nec.

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

7: $icom [licom]$ – Integer Communication Array

On exit: used to communicate details of the task to be carried out to the integration function d02nec.

8: $licom$ – Integer Input

On entry: the dimension of the array icom.

Constraint:

licom \geq neq + 50

9: $com [lcom]$ – double Communication Array

On exit: used to communicate problem parameters to the integration function d02nec. This must be the same communication array as the array com supplied to d02nec. In particular, the values of hmax and h0 are contained in com.

10: $lcom$ – Integer Input

On entry: the dimension of the array com.

Constraints:

the array com must be large enough for the requirements of d02nec. 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 d02npc.

11: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT_ARG_GT: On entry, $licom = 〈value〉$ and $neq = 〈value〉$ .
Constraint: $licom \geq 50 + neq$ .
NE_INT_ARG_LT: On entry, $maxord = 〈value〉$ .
Constraint: $maxord \geq 1$ .

On entry, $neq = 〈value〉$ .
Constraint: $neq \geq 1$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL_ARG_LT: On entry, $hmax = 〈value〉$ .
Constraint: $hmax \geq 0.0$ .

7 Accuracy

Not applicable.

8 Parallelism and Performance

d02mwc 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

10.1 Program Text

Program Text (d02mwce.c)

10.2 Program Data

None.

10.3 Program Results

Program Results (d02mwce.r)

NAG Library Manual, Mark 27

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

D02 (Ode) Chapter Contents

D02 (Ode) Chapter Introduction

d02mw: FL CL CPP AD

NAG CL Interfaced02mwc (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 CL Interface
d02mwc (dae_dassl_setup)