A reliable numeric analytic technique for improving the solution of nonlinear chaotic and hyperchaotic problems - Chowdhury, Md. Sazzad Hossien; Razali, Nur Isnida; Hashim, Ishak; Abdul Majid, Zanariah (2015)
In this study, the multistage homotopy-perturbation method (MHPM) is applied to the nonlinear chaotic Lü system and hyperchaotic Chen and Lorenz system. MHPM is a technique adapted from the standard homotopy- perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the MHPM technique applied in this work, the results are compared with a fourth-order Runge-Kutta method and the standard HPM. The MHPM is tested for several examples. Numerical comparisons demonstrate the limitations of HPM and promising capability of the MHPM for solving chaotic and hyperchaotic systems. The results obtained with minimum amount of computational work show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems.