The use of sparse matrix techniques in ode — Codes

Abstract

Problems involving large systems of ordinary differential equations with sparse Jacobian matrices can be solved efficiently using low-order L-stable one-step methods. Sparse matrix techniques are applied to reduce computational work and to save storage when solving the large systems of linear equations that arise. Variable stepsize strategies have to be used as the systems of ODE's are normally stiff. Iterative refinement is used in connection with incomplete factorisations obtained from the use of drop-tolerances during the factorisation process. This combination leads to reductions in both storage consumption and in the number of evaluations of the Jacobian matrix that has to be performed. Evidence of the efficiency of the strategies involved are given in the form of numerical results from a FORTRAN program package SPARKS that employs a semi implicit Runge-Kutta method.