A Comparative Study of Two Spatial Discretization Schemes for Advection Equation Keywords Advection Equation, Finite Difference Method, The Method of Lines, Von Neumann Method

Abstract In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both discretization techniques approximate correctly solution of advection equation and compare their accuracy and performance