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The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model. (English) Zbl 1023.65109

Summary: Systems of linear and nonlinear partial differential equations and the reaction-diffusion Brusselator model are handled by applying the decomposition method. The advantage of this work is twofold. Firstly, the decomposition method reduces the computational work. Secondly, in comparison with existing techniques, the decomposition method is an improvement with regard to its accuracy and rapid convergence. The decomposition method has the advantage of being more concise for analytical and numerical purposes.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
35L45 Initial value problems for first-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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