Error Bounds on the Solutions of Parabolic Differential Equations

Abstract

Parabolic partial differential equations describe various physical phenomena. Quite frequently, for computational convenience or for lack of information, the coefficients appearing in these equations are represented by their approximate values. Effects of such approximations on the solution can be determined by adequate error bounds. Easily computable estimates of error are obtained for a class of linear equations in two variables. These bounds may be computed without a knowledge of the approximate solution, enabling one to estimate the effect of an approximation in advance. In the process, a solution scheme is also developed. Results are illustrated by considering migration of radionuclides in an idealized waste disposal vault model.