CONSISTENCY, STABILITY AND CONVERGENCE OF FINITE DIFFERENCE SCHEMES ON THE HEAT EQUATION

Abstract

This paper deal with a numerical method for the solution of the heat equation together with initial condition and Dirichlet boundary conditions. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The consistency and the stability of the schemes are described. Futhermore, numerical simulations are performed to illustrate the accuracy and stability of the regularized solution.