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Numerical solution of evolution equations by the Haar wavelet method. (English) Zbl 1110.65097

Summary: An efficient numerical method for the solution of nonlinear evolution equations based on the Haar wavelets approach is proposed. The method is tested in the case of Burgers and sine-Gordon equations. Numerical results, obtained by computer simulation, are compared with other available solutions. These calculations demonstrate that the accuracy of the Haar wavelet solutions is quite high even in the case of a small number of grid points.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65T60 Numerical methods for wavelets
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