In this paper, analytic solutions of two-dimensional coupled Burgers’ equations are obtained by the Homotopy analysis and the Homotopy Pade methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] Homotopy Pade technique is often independent of auxiliary parameter and this technique accelerate the convergence of the related series.

In this article, the Homotopy Perturbation Method (HPM) is employed to approximate solutions of a modified Lotka–Volterra equation. HPM has been introduced by He to solve approximately linear or nonlinear differential equations. Approximate polynomials have also been constructed to find approximate solutions of a modified Lotka-Volterra system. Numerical comparisons are made between HPM and maple numerical results.

In this paper, analytic solutions of the modified Burgers-Korteweg-de Vries equation (mBKdVE) and the Newell -Whitehead equation are obtained by the Ho-motopy analysis method (HAM) and the Homotopy Pade method (HPadeM). The obtained approximation by using HAM contains an auxiliary parameter which is a way to control and adjust the convergence region and rate of the solution series.The approximation solution by [m; m] HPadeM is often independent of auxiliary parameter`h and this technique accelerate the convergence of the related series.

In this paper, optimal Homotopy asymptotic method (OHAM) and multistage op-timal Homotopy asymptotic (MOHAM) method are applied to , nd an approximate solution to Abel's integral equation, that is in fact a weakly singular Volterra inte-gral equation. To illustrate these approaches one example is presented. The results con, rm the e, ciency and ability of these methods to such equations. The results will be compared with the exact solution to , nd out that which method of these two is more accurate.