Finite Volume Method for Solving Two Dimensional Parabolic Initial Bound ary Value Problem

Abstract

In this thesis a finite volume method (FVM) is used to solve two dimensional parabolic initial boundary value problem. The stability analysis of the method was validated with the Von Neumann stability analysis. The efficiency of the proposed method was demonstrated by solving different test problems. Based on the numerical results, the proposed method is well suited for solving two dimensional parabolic initial boundary value problem and the obtained numerical solution by FVM is compared with the exact solutions to check the accuracy of the formulated scheme. Therefore, we came to the conclusion that the method is very promising, efficient and powerful than other methods in terms of providing relatively small errors.