Hopscotch: a Fast Second-order Partial Differential Equation Solver

Present address: IBM (United Kingdom) Ltd., Peterlee, Co. Durham, England. An idea of Gordon for the numerical solution of evolutionaryproblems is reformulated and shown to be equivalent to a Peaceman-Rachfordprocess. A fast computational process is then developed andapplied to parabolic and elliptic problems, both linear andnon-linear. This algorithm is very efficient with regard tocomputing time, storage requirements and ease of programming.Several fairly general conditions are given which ensure convergencefor parabolic and elliptic problems.