Wave propagation analysis of the upwind methods for the solution of one-dimensional advection equation

A variety of explicit and implicit finite difference methods involving two and three levels in time, have been used for solving advection equation ,for example, first , second and third – order upwind formula, Rusanove (1,5) ,Leapfrogsecond and fourth –order, etc. Since the most of accuracy of those methods have not been estimated by wavepropagation analysis ,therefore, In this paper the accuracy of the first ,second and third –order upwind formula forsolving advection equation are studied by wave propagation analysis .Their accuracy has been estimated by comparing their amplitude response and relative wave speed or phase. The results are shown by figures in each case ,to illustrate the efficiency of upwind methods, especially for third-order

Keywords:

finite difference , amplitude respons , wave speed , upwind mthods