The Effect of Spacewise Lumping on the Solution Accuracy of the One-Dimensional Diffusion Equation

Abstract

Numerical or semidiscrete analog approximations to the diffusion equation must be formulated for solutions with automatic computing equipment. The present paper is devoted to the evaluation of truncation errors inherent in the spacewise difference formulation of the equation under general boundary conditions. A general method of analysis is developed and the error between the semidiscrete solution and the exact solution of the partial differential equations is evolved by matrix algebra and the Laplace transform. The method is illustrated by example showing the errors in the case of a symmetrically heated slab subject to temperature boundary conditions expressed as polynomials in time.