Application of multistage homotopy perturbation method to the chaotic Genesio system (Q437672)

Summary: Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM) is applied to the chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM). The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4) solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.