Variational iteration method as a reliable treatment for the hyperchaotic rössler system

Abstract

This paper concerns the implementation of variational iteration method (VIM) in solving the hyperchaotic Rössler analytically. It is a four dimensional system of ODEs with quadratic nonlinearities. The computation was made using a newly found version called the multistage VIM (MVIM) which offers some slight modification to the traditional VIM. Numerical comparisons are made between MVIM and the classical fourth-order Runge-Kutta (RK4) with results displaying extremely good performance by MVIM, yielding great accuracy and efficiency. It is also evident that MVIM surpasses (in terms of accuracy) its two counterparts, the Adomian decomposition method (ADM) and Differential transformation method (DTM).