The space–time Sinc‐Gallerkin method for parabolic problems

Abstract

Abstract This paper contains the formulation of a space–time Sinc‐Galerkin method for the numerical solution of the parabolic partial differential equation in one space dimension. The space–time adjective means that the Galerkin technique is employed simultaneously in time and space. Salient features of the method include: exponential rate of convergence, ease of assembly of the discrete system, a global approximation and the ability to handle singular problems. Two methods of solution for the discrete system are offered and numerical results for test problems, selected from the literature, are included.