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Comparison of the solutions obtained by Adomian decomposition and wavelet-Galerkin methods of boundary-value problems. (English) Zbl 1117.65136

Summary: We compare the performance of Adomian decomposition method and the wavelet-Galerkin method applied to the solution of boundary-value problems involving non-homogeneous heat and wave equations. It is shown that the Adomian decomposition method in many instances gives better results. In the wavelet-Galerkin solutions, Daubechies six wavelets are used because they give better results than those of lower degree wavelets. The results are then compared with those obtained using the Adomian decomposition method. Although the Adomian decomposition solution required slightly more computational effort than the wavelet-Galerkin solution, it results in more accurate results than the wavelet-Galerkin method.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35L05 Wave equation
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