ABSTRACT
This chapter deals with finite difference methods. It briefly introduces the hyperbolic problems, presents some basic finite difference schemes for the convection problem, and reviews the von Neumann stability analysis technique. The chapter also introduces the important concepts on dissipation and dispersion errors, and extends the development of various finite difference schemes to conservation laws and the second-order hyperbolic problems. It demonstrates how to develop and analyze the schemes for solving the second-order hyperbolic equations where discussions are subdivided into the 1-D and 2-D subsections. The chapter presents a MATLAB code to solve the convection problem using the Lax-Wendroff scheme.
