Stiff PDE in heat problem : solution using the method of lines with new numerical algorithm

Abstract

An equation where solutions change on two vastly different scales will encounter a stiff problem. Partial differential equations can lead to systems of first order ordinary differential equations when discretized using finite difference such as methods of lines. The method of lines, (MOL) is a powerful technique for solving partial differential equation. This project aims to demonstrate the combination of two methods in order to solve the stiff problems. The methods are the method of lines with five-points central finite difference and the explicit third order Runge-Kutta method.