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