Numerical Simulation of Partial Differential Equations Using Finite Difference Methods

Abstract

This paper explores the use of the software package, Matlab and Excel in the implementation of the finite difference method to solve partial differential equations (PDE’s.). It aimed to examine the strength of the forward explicit method and backward implicit method in solving PDE’s. A comparison was made between the forward explicit method and the backward implicit method for their stability. The FDM method was used to solve partial differential equations of heat. Numerical examples were also created and analysed to show the strengths of each method. The results shows that the forward explicit method is conditionally stable because the stability it requires a small step size of time ‘t’ compared to space ‘x’ for stability. The backward implicit method is unconditionally stable because it depends on the local truncation error considerations.