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5 One Dimensional Problem

The one dimensional wave equation with a homogeneous velocity function has an analytic solution [22]. The wave propagates in two directions; solutions are of the form . The method of characteristics can be used to formulate this analytic solution. The numerical solution [10] has the advantage of solving the inhomogeneous problem, which is awkward analytically but feasible in one dimension. After mastering the requirements of one dimensional modeling, the extensions required for two and three dimensional models are not difficult. Inhomogeneous modeling in two and three dimensions requires a numerical method; analytic methods are not capable of modeling most complex media.