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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.

65P20Numerical chaos
65L20Stability and convergence of numerical methods for ODE
37D45Strange attractors, chaotic dynamics
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
Full Text: DOI
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