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Comparing numerical methods for the solutions of the Chen system. (English) Zbl 1131.65101
Summary: The Adomian decomposition method (ADM) is applied to the Chen system [cf. G. Chen and T. Ueta, Int. 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. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given.

65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
37M05 Simulation of dynamical systems
Zbl 0962.37013
Full Text: DOI
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