Numerical methods for simulation of large systems

Abstract

The numerical solution of large initial value problems, including those that are derived as approximations to systems of partial differential equations, may encounter difficulties using conventional numerical methods because of stiffness (large range of eigenvalues of the associated linear system). In a nonlinear system, the eigenvalues may change greatly during the solution and a system that is initially well behaved may become stiff, yielding increased computer cost or inaccuracies. This paper contains a discussion of various definitions of stiffness, and several methods for overcoming it, including a new method for identifying and partitioning a two-time-scale system into fast and slow sub-systems. Also included are some experiences using the DARE continuous system simulation language for systems as large as 200 coupled nonlinear ordinary differential equations.