A comparison of several methods of integrating stiff ordinary differential equations on parallel computing architectures

Abstract

Many physical systems lead to initial value problems where the system of stiff ordinary differential equations is loosely coupled. Thus, in some cases the variables may be directly mapped onto sparsely connected parallel architectures such as the hypercube. This paper investigates various methods of implementing Gear's algorithm on parallel computers. Two conventional corrector methods utilize either functional or Newton Raphson iteration. We consider both alternatives and show that they exhibit similar speedups on an n node hypercube. In addition a polynomial corrector is investigated. It has the advantage of not having to solve a linear system as in the Newton Raphson method, yet it converges faster than functional iteration.