VSMRK: A Parallel Implementation and the Performance of Variable Stepsize Multistep Runge-Kutta Methods for Stiff ODEs

摘要

Many natural phenomena and applications in industry can be modeled as systems of Stiff Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs). Usually the problems to be solved are huge in dimension, hence require huge computing resources and time. This study describes the parallel implementation of Variable stepsize Multistep Runge-Kutta (MRK) method of Radau Type for solving stiff IVPs of ODEs and its performance on SGI Origin 2000. The numerical results show the superiority of the code compared to various standard code on dense and large sparse problems.