Numerical Solutions of the Equal Width Wave Equation Using an Adaptive Method of Lines

The equal-width wave (EW) equation is a model partial differential equa- tion for the simulation of one-dimensional wave propagation in media with nonlinear wave steepening and dispersion processes. The background of the EW equation is reviewed and this equation is solved by using an advanced numerical method of lines with an adaptive grid whose node movement is based on an equidistribution princi- ple. The solution procedure is described and the performance of the solution method is assessed by means of computed solutions and error measures. Many numerical solutions are presented to illustrate important features of the propagation of a solitary wave, the inelastic interaction between two solitary waves, the breakup of a Gaussian pulse into solitary waves, and the development of an undular bore.

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