Using Diagonally Implicit Multistage Integration Methods for Solving OrdinaryDifferential Equations. Part 1: Introduction and Explicit Methods

摘要

A survey of theoretical results for the recently invented and highly promisingclass of diagonally implicit multistage integration methods (DIMSIMs) is provided. New results are obtained that provide improved implementation and simplified analysis. Particular attention is given to issues affecting use on parallel computers in waveform relaxation. The process of implementation parameter derivation and testing for the second and fifth order members of the DIMEX family of ordinary differential equation solver computer codes using explicit DIMSIMs is described. Extensive test results using the standard suite DETEST are reported that show considerable promise. A listing of the FORTRAN 77 research code DIMEX5 is provided.