Solution of the Differential-Difference Equations by Optimal Homotopy Asymptotic Method

Abstract

We applied a new analytic approximate technique, optimal homotopy asymptotic method (OHAM), for treatment of differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Volterra equation in different form. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier, and explicit.

An extension of the optimal homotopy asymptotic method with applications to nonlinear coupled partial differential equations

“…The motivation of this paper is to implement the EOHAM for the solution of coupled PDEs. In [10][11][12][13][14][15][16] OHAM has been proved to be valuable for obtaining an approximate solution of single partial differential equation (PDE). In the succeeding section, the basic idea of EOHAM is formulated for the solution of NPDEs.…”

Analytical solution of the viscous flow over a stretching sheet by multi-step optimal homotopy asymptotic method

“…These methods also required the initial guess. We have modified the OHAM [11,15,[22][23][24][25] for large domain.…”

MHD boundary layer flow of an incompressible upper convected Maxwell fluid by Optimal Homotopy Asymptotic Method.

“…Most of the MHD problems are nonlinear and strongly nonlinear. An enormous amount of research work has been invested in the study of nonlinear problems [20][21][22][23][24]. In this article, we shall deal with the MHD Maxwell ow problem, a strongly nonlinear boundary value problem [25].…”