Enhanced variational iteration method using adomian polynomials for solving the chaotic lorenz system

A merger of two numeric-analytic methods poses various challenges, but also holds promise. Such a fusion could enhance the performance of calculations and may also overcome certain drawbacks of each used individually. This paper focuses on solving the chaotic Lorenz system, a three-dimensional system of ordinary differential equations with quadratic nonlinearities, using a newly designed hybrid algorithm merging multistage variational iteration method with Adomian polynomials. The core of this algorithm is made by surrogating the nonlinear terms in the variational iteration method with Adomian polynomials. Numerical comparisons are made between the hybrid and the classic fourth-order Runge-Kutta method. Our work demonstrates that the multistage hybrid provides good accuracy and efficiency for the chaotic Lorenz system.