The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system

In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is presented. The HPM is treated as an algorithm in a sequence of intervals (i.e. time step) for finding accurate approximate solutions to the famous Lorenz system. Numerical comparisons between the multistage homotopy-perturbation method (MHPM) and the classical fourth-order Runge–Kutta (RK4) method reveal that the new technique is a promising tool for the nonlinear systems of ODEs.