ABSTRACT
In this chapter, we will continue our discussion on finite difference methods. In Sec. 3.1, we briefly introduce the hyperbolic problems. Then in Sec. 3.2, we present some basic finite difference schemes for the convection problem and review the von Neumann stability analysis technique. We introduce the important concepts on dissipation and dispersion errors in Sec. 3.3. We extend the development of various finite difference schemes to conservation laws and the second-order hyperbolic problems in Sec. 3.4 and Sec. 3.5, respectively. In Sec. 3.6, we present a MATLAB code to solve the convection problem using the Lax-Wendroff scheme.
