In this paper, we apply Homotopy Analysis Transform Method (HATM) for solving various nonlinear equations. This method is the combined for of the homotopy analysis method and Laplace transform method. HATM is applied without any discretization or restrictive assumption and avoids roundoff errors which may lead the solution in closed form. The results reveal that the HATM is very effective, conv...

In this paper, an application of Homotopy Analysis Method (HAM) is applied to solve the equation governing the unsteady flow of a polytropic gas. Comparison are made between the Adomian decomposition method and homotopy analysis method. The results reveal that the homotopy analysis method is very effective and simp le and gives the exact solution. Classification 2000 MSC: 34K28 • 35G25 • 34K17

Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizi...

We give new versions of the global Newton method and the Kellogg & Li & Yorke method for calculating zero points and fixed points of nonlinear maps, which are numerically stable, but do not require an extra homotopy dimension. In addition, regularity results are established so that predictor-corrector continuation methods will lead to solutions if appropriate boundary conditions are satisfied.

We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series w...

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa–Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu & Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & ...