Standard Homotopy Perturbation Method Research Articles

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.

On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model

The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by an adaptation of the standard analytic homotopy-perturbation method (HPM). The standard HPM is converted into a hybrid numeric–analytic method called the multistage HPM (MHPM). The numerical results obtained from the MHPM and the classical fourth-order Runge–Kutta (RK4) method are in complete agreement.

Application of multistage homotopy-perturbation method for the solutions of the Chen system

In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chen system. We shall call this technique as the multistage HPM (for short MHPM). In particular we look at the accuracy of the HPM as the Chen system changes from a nonchaotic system to a chaotic one. Numerical comparisons between the MHPM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear chaotic and nonchaotic systems of ODEs.

Adaptation of homotopy-perturbation method for numeric–analytic solution of system of ODEs

Abstract A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact solution and the classical fourth-order Runge–Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.