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A piecewise-spectral parametric iteration method for solving the nonlinear chaotic Genesio system. (English) Zbl 1225.65120

Summary: An effective algorithm which is a combination of the spectral collocation method and the parametric iteration method (PIM) is proposed for simulating the solution of the chaotic Genesio system (CGS). Comparison with the fourth-order Runge-Kutta method (RK4) confirms the very high accuracy of the presented algorithm. The obtained results reveal that the proposed algorithm is a promising method for the solution of the CGS and more promising because it can further be readily employed to solve other chaotic systems.

MSC:

65P20 Numerical chaos
65L20 Stability and convergence of numerical methods for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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