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Zbl 1225.65120
Ghorbani, A.; Saberi-Nadjafi, J.
A piecewise-spectral parametric iteration method for solving the nonlinear chaotic Genesio system. (English)
[J] Math. Comput. Modelling 54, No. 1-2, 131-139 (2011). ISSN 0895-7177

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 2000:: *65P20 Numerical chaos
65L20 Stability of numerical methods for ODE
37D45 Strange attractors, chaotic dynamics
65L60 Finite numerical methods for ODE

Keywords: piecewise-spectral PIM; spectral collocation; convergence theorem; valid/stability region; Runge-Kutta method; chaotic Genesio system

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Zentralblatt MATH Berlin [Germany]