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On solving the chaotic Chen system: A new time marching design for the variational iteration method using Adomian’s polynomial. (English) Zbl 1190.65189
Summary: This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving the chaotic Chen system [cf. G. Chen and T. Ueta, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 7, 1465–1466 (1999; Zbl 0962.37013)] which is a three-dimensional system of ordinary differential equations with quadratic nonlinearities. This research implements the multistage variational iteration method with an emphasis on the new multistage hybrid of variational iteration method with Adomian polynomials. Numerical comparisons are made between the multistage variational iteration method, the multistage variational iteration method using the Adomian’s polynomials and the classic fourth-order Runge-Kutta method. Our work shows that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage variational iteration method.

MSC:
65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
37M05 Simulation of dynamical systems
Citations:
Zbl 0962.37013
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