On the use of implicit method for solving parabolic PDE temperature in a slender road

Abstract

In this paper, we discuss the “finite difference method” (FDM) to solve temperature distribution with Implicit Method. The temperature distribution in a slender rod of unit length has been described by the one- dimensional heat equation. The finite difference method (FDM) seems to be the simplest approach for the numerical solution of PDEs. The partial-derivatives are replaced by ‘finite difference approximations’ that lead to a system of linear algebraic equations. In the process we introduce important concepts as stability used in analyzing finite difference methods and to show how to solve parabolic equations.