NAG Library Function Document

nag_dae_ivp_dassl_setup (d02mwc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{neq}$ – IntegerInput

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

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

2:    $\mathbf{maxord}$ – 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:    $\mathbf{jceval}$ – Nag_EvaluateJacobianInput

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

$\mathbf{jceval}=\mathrm{Nag\_NumericalJacobian}$

The Jacobian is to be evaluated numerically by the integrator.

$\mathbf{jceval}=\mathrm{Nag\_AnalyticalJacobian}$

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

Constraint: $\mathbf{jceval}=\mathrm{Nag\_NumericalJacobian}$ or $\mathrm{Nag\_AnalyticalJacobian}$.

4:    $\mathbf{hmax}$ – doubleInput

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:    $\mathbf{h0}$ – doubleInput

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:    $\mathbf{vector\_tol}$ – Nag_BooleanInput

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

$\mathbf{vector\_tol}=\mathrm{Nag\_FALSE}$

rtol and atol are single element vectors.

$\mathbf{vector\_tol}=\mathrm{Nag\_TRUE}$

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:    $\mathbf{icom}\left[\mathbf{licom}\right]$ – 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:    $\mathbf{licom}$ – IntegerInput

On entry: the dimension of the array icom.

Constraint: $\mathbf{licom}\ge \mathbf{neq}+50$.

9:    $\mathbf{com}\left[\mathbf{lcom}\right]$ – 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:  $\mathbf{lcom}$ – 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, $\mathbf{lcom}\ge 40+\left(\mathbf{maxord}+4\right)\times \mathbf{neq}+{\mathbf{neq}}^2$;
• 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 nag_dae_ivp_dassl_linalg (d02npc).

11:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT_ARG_GT

On entry, $\mathbf{licom}=〈\mathit{\text{value}}〉$ and $\mathbf{neq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{licom}\ge 50+\mathbf{neq}$.

NE_INT_ARG_LT

On entry, $\mathbf{maxord}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{maxord}\ge 1$.

On entry, $\mathbf{neq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{neq}\ge 1$.

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL_ARG_LT

On entry, $\mathbf{hmax}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{hmax}\ge 0.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d02mwce.c)

10.2

Program Data

10.3

Program Results

Program Results (d02mwce.r)