A composite integration scheme for the numerical solution of systems of ordinary differential equations

摘要

A generalization of a composite linear multistep method [2] is developed and applied to the approximate integration of systems of ordinary differential equations. The proposed scheme is second-order accurate and L-stable. An algorithm, based on the integration formula derived in this paper, is applied to approximate the solutions of a number of standard test problems. The numerical results indicate that the method is competitive with other fixed-order methods particularly in terms of computational overhead and could provide the basis for efficient temporal integration in the semidiscretization of time dependent partial differential equations.