The efficient solution of linear constant-coefficient systems of differential equations

Abstract

Most numerical techniques that have been proposed for the solution of constant-coefficient linear prob- Zems involve -either directly or indirectly-approxi mating a matrix exponential. For large systems these techniques can be very expensive to implement on digital computers. In this paper we describe how standard stiff ordinary differential equation (ODE) methods can be modified to take advantage of linear ity and thereby efficiently solve large linear prob lems. Methods based on backward differentiation formulas or second derivative formulas are particular ly suitable for this purpose. The implementation of these methods is discussed and numerical results are presented.