Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

Abstract

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us 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.…”

Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations

“…The motivation of this paper is to formulate and implement the (MOHAM) for the solution of system of (PDEs). In [19][20][21][22][23], (OHAM) has been proved to be valuable for obtaining approximate solutions of various boundary value problems. Here we have proved that (MOHAM) is useful H. Ullah et al / Eur.…”