Numerical Solution of a One Dimensional Heat Equation with Dirichlet Boundary Conditions

Abstract

In this paper I present Numerical solutions of a one dimensional heat Equation together with initial condition and Dirichlet boundary conditions. Two methods are used to compute the numerical solutions, viz. Finite difference methods and Finite element methods. The finite element methods are implemented by Crank - Nicolson method. The numerical solutions of a one dimensional heat Equation together with initial condition and Dirichlet boundary conditions using finite difference methods do not always converge to the exact solutions. It indicates the occurrence of numerical instability in finite difference methods. Finally the numerical solutions obtained by these two methods are compared with the analytic solutions graphically into two and three dimensions.