Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are illustrated for prototypical nonline...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

This article is an analysis of fractional nonlinear convection–reaction–diffusion equations involving the Atangana–Baleanu and Caputo derivatives. An efficient Aboodh homotopy perturbation transform method, which combines method with transformation, applied to investigate this fractional-order proposed model, analytically. A modified technique known as formulated approximate these The analytica...

The homotopy analysis method (HAM) is a useful to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein–Weyl coupled with Maxwell field and obtain approximation for charged by using HAM. It found that are sufficiently accurate entire spacetime outside hole’s event horizon also consistent numerical ones Einstein–Maxwell–Weyl gra...

In this paper, the Homotopy Analysis Method (HAM) is presented for obtaining the approximate solution of new coupled modified Korteweg-de Vries (MKdV) system. The approximate analytical solution is obtained by using this method in the form of a convergent power series with components that are easily computable. For the problems considered, only a few terms are required to obtain an approximate ...

The homotopy perturbation method (HPM) is employed successfully for solving the modified Korteweg-de Vries equation. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or perturbation theory. The results show applicability, accuracy and efficiency of the HPM i...

This paper investigates the implementation of Variational Iteration Method (VIM) to practical and higher order nonlinear equations in kind of Korteweg-de-Vries (KdV) equation. The obtained solutions from thirdand fourth-order modified KdV are compared with the exact and Homotopy Perturbation Method (HPM) solutions. Results illustrate the efficiency and capability of VIM to solve high order nonl...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...