A THIRD ORDER FINITE-DIFFERENCE METHOD FOR TWO DIMENSIONAL PARABOLIC EQUATIONS

Abstract

This chapter discusses a third-order finite-difference method for two dimensional parabolic equations. Parabolic partial differential equations represent a class of problems of great importance in many fields of engineering and science. When the need for a numerical solution of such problems arises, the requirements for computing time and storage capacity often tax the capabilities of today's largest digital computer. Thus, the need of more efficient numerical methods is an ever constant one. When solving numerically a two dimensional parabolic partial differential equation, it is always advantageous, if not desirable, to use splitting methods. The chapter discusses difference scheme for the solution of two dimensional parabolic equation. It also presents the results of numerical experiments and their explanations using the method.