On solving the chaotic Chen system: a new time marching design for the variational iteration method using Adomian's polynomial

This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving the chaotic Chen system, which is a three-dimensional system of ODEs 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.