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Hyperbolic partial differential equations are used to model a large and extremely important collection of phenomena. This includes aerodynamic flows, flows of fluids and contaminants through a porous media, atmospheric flows, etc. The solutions to hyperbolic equations tend to be more complex and interesting than those to parabolic and elliptic equations. The interesting characteristics of the solutions to hyperbolic equations follows from the fact that the phenomena modeled by hyperbolic equations are generally difficult and interesting. Of course, most of the applications mentioned above involve nonlinear systems of equations. However, most techniques for solving nonlinear systems are generalizations of or are otherwise related to some linear technique. For this reason, we begin by considering linear systems of hyperbolic equations.
KeywordsPartial Differential Equation Difference Scheme Periodic Boundary Condition Discrete Fourier Transform Hyperbolic Equation
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