NAG Library Sub-chapter Introduction

d02m–n – Integrators for Stiff Ordinary Differential Systems



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, Ft,y,y=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 Ft,y,y=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
fx + 1-t gx = 0  
where the solution to fx +gx = 0  is known. The solution of this type of problem is illustrated in Section 10 in nag_dae_ivp_dassl_gen (d02nec).


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
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017