Comparative Analysis of FTCS, Richardson, and Dufort-Frankel Numerical Methods for Temperature Distribution in a One-Dimensional Rod

Abstract

This Forward Time Centred Space (FTCS), Richardson, and Dufort-Frankel finite difference methods for solving the one-dimensional heat conduction equation are examined and compared in this paper.  The goal is to evaluate each method's accuracy, stability, and computational efficiency by analysing the temperature distribution along a rod.  To put the approaches into action, the same starting and ending points for each were used.  Not only is FTCS simple and quick to construct, but the results also show that it is conditionally stable.  Despite its improved accuracy, Richardson is prone to numerical instability.  While the Dufort-Frankel approach is more complicated, it provides better stability.  The results help with thermal simulation application requirements-based method selection.