Abstract
In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions.
Highlights
The application of the homotopy perturbation method in non-linear problems has been developed by scientists and engineers, because this method continuously deforms the difficult problem under study into a simple problem which is easier to solve
The homotopy perturbation method is a coupling of the traditional perturbation method and the homotopy method in topology [6]
The paper is organized as follows: In Section 2, we present a brief summary about the homotopy perturbation method
Summary
The application of the homotopy perturbation method in non-linear problems has been developed by scientists and engineers, because this method continuously deforms the difficult problem under study into a simple problem which is easier to solve. Several methods have been used to find approximate solutions to nonlinear problems, such as, the homotopy perturbation method [2]-[7], the variational iteration method [8]-[10], and the energy balance method [11]-[14]. The principles of the variational iteration method and its applicability for various kinds of differential equations are given in [8] [15]-[19]. In this method, it is required first to determine the Lagrange multiplier λ optimally.
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