HYBRID THE SINE–COSINE WAVELET AND FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR BELOUSOV–ZHABOTINSKY REACTION SYSTEM

HYBRID THE SINE–COSINE WAVELET AND FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR BELOUSOV–ZHABOTINSKY REACTION SYSTEM

S. Foadian, R. Pourgholi

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Abstract

In this paper, a numerical method for solving the nonlinear Belousov– Zhabotinsky reaction system is proposed. The method is based on hybrid function approximations. In the solution process, the time derivative is discretized by the finite difference method, the spatial discretization is made by Sine–Cosine wavelets, and the nonlinear terms are linearized by the quasilinearization technique. Also, the convergence analysis of the proposed method has been discussed. Finally, to show the efficiency and accuracy of the method in solving this system, an illustrative example is included and the results are compared with the Haar wavelet method.

Keywords

Nonlinear Belousov–Zhabotinsky system, Sine–Cosine wavelets method, Finite difference method, Operational matrix, Convergence analysis.