A Comparison of Time Discretization Schemes in the Solution of a Convection-Difussion Equation

Abstract

The aim of this work is to present in a didactic way a comparison of analytical and numerical solutions of a transient one-dimensional heat transfer problem. So, the solution of a parabolic equation of convection-diffusion type has been done with discretization in space by the Central Finite Difference method and in the time by five schemes: two explicit and three implicit. From the analytical and the numerical results the L2 norm and the L-infinity norm are evaluated as measures of the error. Some numerical applications are presented and discussed.