Solution of ordinary differential initial value problems on an intel hypercube

Abstract

Schemes for the solution of linear initial or boundary value problems on a hypercube were developed by Katti and Neta [1] and tested and improved by Lustman, Neta and Katti [2]. Among other procedures for parallel computers, fully implicit Runge-Kutta methods were discussed by Jackson and Norsett [3] and Lie [4]. Here, we develop a method based on extrapolation to the limit, which is useful even for nonlinear problems. Numerical experiments show excellent accuracy when low order schemes are combined with polynomial extrapolation.