1

Introduction

This sub-chapter contains the specifications of the integrators
from the
DASSL package, Brenan et al. (1996).

The DASSL integrator nag_dae_ivp_dassl_gen (d02nec) is designed for solving systems of the form, $F\left(t,y,y\prime \right)=0$. These formulations permit solution of differential/algebraic systems
(DAEs). The facilities provided are essentially those of the explicit solvers.

The DASSL integrator, nag_dae_ivp_dassl_gen (d02nec), has an associated setup function nag_dae_ivp_dassl_setup (d02mwc) which must be called first. On return from the integrator, if it is feasible to continue the integration, the associated continuation call function is nag_dae_ivp_dassl_cont (d02mcc) may be called to rest various integration parameters. The structure of the Jacobian is assumed to be full unless nag_dae_ivp_dassl_linalg (d02npc) is called following a call to the setup function to specify that the Jacobian is banded and to supply its bandwidths.

The DASSL integrator nag_dae_ivp_dassl_gen (d02nec) can solve DAEs of the fully implicit form $F\left(t,y,y\prime \right)=0$ and therefore has increased functionality over the SPRINT integrators. Additionally
nag_dae_ivp_dassl_gen (d02nec) can be used to solve difficult algebraic problems by continuation; for example, the nonlinear algebraic problem

can be solved by integrating solutions of

where the solution to $f\left(x\right)+g\left(x\right)=0$ is known. The solution of this type of problem is illustrated in Section 10 in **nag_dae_ivp_dassl_gen (d02nec)**.

$$f\left(x\right)=0$$ |

$$f\left(x\right)+\left(1-t\right)g\left(x\right)=0$$ |

2

References

Berzins M and Furzeland R M (1985) A user's manual for SPRINT – A versatile software package for solving systems of algebraic, ordinary and partial differential equations: Part 1 – Algebraic and ordinary differential equations *Report TNER.85.085* Shell Research Limited

Brenan K, Campbell S and Petzold L (1996) *Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations* SIAM, Philadelphia