185 - Hyperbolic Equations: Method of Characteristics

Abstract

This chapter focuses on the method of characteristics applicable to single hyperbolic equation, or a system of hyperbolic equations. A numerical approximation scheme is obtained. The method of characteristics can be used directly to create a numerical scheme to integrate hyperbolic equations. The method on the second-order hyperbolic partial differential equation is illustrated. The numerical procedure is now a straightforward application of the method of characteristics. The procedure can be made more concise by use of matrix notation. This technique can be readily modified to work with systems of hyperbolic equations. This technique is sometimes considered to be superior to using finite differences directly, because it utilizes the mathematical structure of the solution.