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Applied Mathematics and Computation. 01/2007; 186:1701-1709.
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Applied Mathematics and Computation. 01/2007; 187:1056-1062.
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Applied Mathematics and Computation. 01/2007; 188:1419-1425.
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ABSTRACT: In this article the problem of prey and predator is presented and the homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear Volterra differential equations governing on the problem. The results are compared with the results using the Adomian decomposition and the power series methods. Some plots are presented to show the populations of the prey and the predator versus time for illustrating the reliability and simplicity of the method.
Applied Mathematics and Computation.
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ABSTRACT: In this Letter, He's homotopy perturbation method (HPM) is implemented for finding the solitary-wave solutions of the regularized long-wave (RLW) and generalized modified Boussinesq (GMB) equations. We obtain numerical solutions of these equations for the initial conditions. We will show that the convergence of the HPM is faster than those obtained by the Adomian decomposition method (ADM). The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.
Physics Letters A.
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ABSTRACT: In this paper, He's variational iteration method (VIM) is applied to nonlinear oscillators with discontinuities. We illustrate that the VIM is very effective and convenient and does not require linearization or small perturbation. Contrary to the conventional methods, in VIM, only one iteration leads to high accuracy of the solutions. Moreover, we show that the obtained approximate solutions are valid for the whole solution domain and the approximations are uniformly valid not only for small parameters, but also for very large parameters.
Journal of Sound and Vibration.
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ABSTRACT: In this article two problems are considered; the first one is the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of prey and predator. The variational iteration method is employed to compute an approximation to the solutions of the systems of nonlinear ordinary differential equations governing on these problems. The results are compared with the results obtained by Adomian decomposition and power series methods. Some plots are presented to show the reliability and simplicity of the method.
Applied Mathematics and Computation 186(2):1701-1709. · 1.32 Impact Factor
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ABSTRACT: In this Letter, He's homotopy perturbation method (HPM), which does not need small parameter in the equation is implemented for solving the nonlinear Hirota–Satsuma coupled KdV partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of Adomian's decomposition method has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.
Physics Letters A.
