Hopscotch: a Fast Second-order Partial Differential Equation Solver

Abstract

An idea of Gordon for the numerical solution of evolutionary problems is reformulated and shown to be equivalent to a Peaceman-Rachford process. A fast computational process is then developed and applied to parabolic and elliptic problems, both linear and non-linear. This algorithm is very efficient with regard to computing time, storage requirements and ease of programming. Several fairly general conditions are given which ensure convergence for parabolic and elliptic problems.