The Numerical Solution of the Fourth Boundary Value Problem for Parabolic Partial Differential Equations

Abstract

A direct method for the numerical solution of the implicit finite difference equations derived from a parabolic differential equation with periodic spatial boundary conditions is presented in algorithmic from. Consideration is given to the stability of the rounding errors involved in the solution process and numerical results are derived which compare favourably with those obtained from the analytical solution and a matrix spectral resolution method which is closely allied to the method of lines.