A Matricial Exponentially Fitted Scheme for the Numerical Solution of Stiff Initial-Value Problems

Abstract

We present an exponentially fitted scheme for the numerical integration of stiff systems of initial-value problems. The basic algorithm consists of an explicit, one-step method which requires the computation of the exponential of a matrix. This task is achieved using Ward's scaling and squaring algorithm [1]. The results of some numerical experiments are presented which allow an appraisal of the proposed approach with other methods.