On a Continuous Method of Approximating Solutions of the Heat Equation

Abstract

Theoretical methods, based on a priori pointwise bounds, for approximating solutions of many elliptic and parabolic initial and/or boundary value problems, have been developed in recent years. These methods, however, are relatively unknown to potential users since applications of the methods have not appeared in the literature. In this paper their usefulness is illustrated by employing some of the author's theoretical results as a basis for the construction of a digital program to compute an approximate solution of an initial boundary value problem for the heat equation.