d02 Chapter Contents
d02 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_dae_ivp_dassl_setup (d02mwc)

## 1  Purpose

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

## 2  Specification

 #include #include
 void nag_dae_ivp_dassl_setup (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)

## 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.

None.

## 5  Arguments

1:     neqIntegerInput
On entry: the number of differential-algebraic equations to be solved.
Constraint: ${\mathbf{neq}}\ge 1$.
2:     maxordIntegerInput
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:     jcevalNag_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:     hmaxdoubleInput
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:     h0doubleInput
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:     vector_tolNag_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.
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:     licomIntegerInput
On entry: the dimension of the array icom.
Constraint: ${\mathbf{licom}}\ge {\mathbf{neq}}+50$.
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:   lcomIntegerInput
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, ${\mathbf{lcom}}\ge 40+\left({\mathbf{maxord}}+4\right)×{\mathbf{neq}}+{{\mathbf{neq}}}^{2}$;
• if the system Jacobian is banded, ${\mathbf{lcom}}\ge 40+\left({\mathbf{maxord}}+4\right)×{\mathbf{neq}}+\left(2×{\mathbf{ml}}+{\mathbf{mu}}+1\right)×{\mathbf{neq}}+2×\phantom{\rule{0ex}{0ex}}\left({\mathbf{neq}}/\left({\mathbf{ml}}+{\mathbf{mu}}+1\right)+1\right)$.
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:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

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.
NE_REAL_ARG_LT
On entry, ${\mathbf{hmax}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{hmax}}\ge 0.0$.

Not applicable.

Not applicable.

None.

## 10  Example

This example solves the plane pendulum problem, defined by the following equations:
 $x′ = u y′ = v u′ = -λx v′ = -λy-1 x2+y2 = 1.$
Differentiating the algebraic constraint once, a new algebraic constraint is obtained
 $xu+yv=0 .$
Differentiating the algebraic constraint one more time, substituting for ${x}^{\prime }$, ${y}^{\prime }$, ${u}^{\prime }$, ${v}^{\prime }$ and using ${x}^{2}+{y}^{2}-1=0$, the corresponding DAE system includes the differential equations and the algebraic equation in $\lambda$:
 $u2 + v2 - λ - y = 0 .$
We solve the reformulated DAE system
 $y1′ = y3 y2′ = y4 y3′ = -y5×y1 y4′ = -y5×y2-1 y32 + y42 - y5 - y2 = 0.$
For our experiments, we take consistent initial values
 $y10 = 1 , ​ y20 = 0 , ​ y30 = 0 , ​ y40 = 1 ​ and ​ y50 = 1$
at $t=0$.

### 10.1  Program Text

Program Text (d02mwce.c)

None.

### 10.3  Program Results

Program Results (d02mwce.r)