nag_dae_ivp_dassl_setup (d02mwc) : NAG Library, Mark 24

3 Description

This integrator setup function must be called before the first call to the integrator nag_dae_ivp_dassl_gen (d02nec). nag_dae_ivp_dassl_setup (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.

5 Arguments

1: neq – IntegerInput

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

Constraint:

neq \geq 1

2: maxord – IntegerInput

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_EvaluateJacobianInput

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 – doubleInput

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 – doubleInput

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_BooleanInput

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 nag_dae_ivp_dassl_gen (d02nec).

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

7: icom[licom] – IntegerCommunication Array

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

8: licom – IntegerInput

On entry: the dimension of the array icom.

Constraint:

licom \geq neq + 50

9: com[lcom] – doubleCommunication Array

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

10: lcom – IntegerInput

On entry: the dimension of the array com.

Constraints:

the array com must be large enough for the requirements of nag_dae_ivp_dassl_gen (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 nag_dae_ivp_dassl_linalg (d02npc).

11: fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

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.

NE_REAL_ARG_LT

On entry,

hmax = ⟨value⟩

.
Constraint:

hmax \geq 0.0

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

10.2 Program Data

None.

10.3 Program Results

NAG Library Function Document

nag_dae_ivp_dassl_setup (d02mwc)

+− 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 Library Function Documentnag_dae_ivp_dassl_setup (d02mwc)

+− 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 Library Function Document

nag_dae_ivp_dassl_setup (d02mwc)