Examining the Performance of MATLAB’s Matrix Capabilities, Testing on Euler’s Method Applied on the Diffusion Equation

Abstract

When one develops, tests and uses numerical methods to solve a differential equation, the performance of the method depends on the concrete way how the method is implemented and coded. In this tentative work, we solve the linear diffusion equation by the simplest explicit Euler method implemented with for loops as well as the built-in matrix operations of MATLAB. We obtain that the for loop performs better in one space dimension, but the matrix operations are faster in two space dimensions.