In the present work, we apply the variational iteration method using He's polynomials (VIMHP) for solving four examples of the biological population model (BPM). The proposed method is a combination of He's variational iteration and the homotopy perturbation methods. The suggested algorithm is practically more reliable, highly efficient for use in such problems. The proposed method finds the solution without any restrictive assumptions, discretization and linearization. The approximate solution converges very rapidly to the exact solution which confirms the accuracy of this method as an easy algorithm for computing the solution for wider classes of linear and nonlinear differential equations.
This paper deals with implementation of the variational homotopy pertubation method (VHPM) for solving the K(2,2) compacton equation. The numerical results show that the approach is easy to implement and accurate when it is compared with the exact solution. The suggested algorithm is quite efficient and is practically well suited for use in the nonlinear problems. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.
In the present work, we apply an analytical method known as Homotopy Perturbation Transform Method, is used for solving Newell-Whitehead-Segel Equation. Five tests are examined to validate the accuracy of this algorithm. Numerical results show that the proposed method is a more reliable, efficient and convenient one for solving different cases of Newell-Whitehead-Segel equation.
In this paper, variational homotopy perturbation method (VHPM) is applied for solving the foam drainage equation with time and space-fractional derivatives. Numerical solutions are obtained for various values of the time and space-order derivative in (0,1]. For the first-order time and space derivative, compared with the exact solution, the result showed that the proposed method could be used as an alternative method for obtaining an analytic and approximate solution for different types of differential equations.
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