We describe, very briefly, the basic ideas and current developments of the homotopy
analysis method, an analytic approach to get convergent series solutions of strongly …

As it is described in the frame work of the homotopy analysis method (HAM), the
convergence-control parameter is the main auxiliary tool which distinguishes this method …

We present here a 'similar'solution for the nano boundary layer with nonlinear Navier
boundary condition. Three types of flows are considered:(i) the flow past a wedge;(ii) the …

In this study, a reliable approach for convergence of the homotopy analysis method when
applied to nonlinear problems is discussed. First, we present an alternative framework of the …

The purpose of the present paper is to introduce a method, probably for the first time, to
predict the multiplicity of the solutions of nonlinear boundary value problems. This procedure …

A new transform, namely the homotopy transform, is defined for the first time. Then, it is
proved that the famous Euler transform is only a special case of the so-called homotopy …

A non-linear coupled-mode system of horizontal equations is presented, modelling the
evolution of nonlinear water waves in finite depth over a general bottom topography. The …

In this paper, we use homotopy analysis method (HAM) to solve two‐point nonlinear
boundary value problems that have at least one solution. The new approach provides the …

This paper shows that the homotopy analysis method, the well-known method to solve ODEs
and PDEs, can be applied as well as to solve linear and nonlinear integral equations with …

The purpose of the present paper is to give a proof for a systematic method namely,
predictor homotopy analysis method (PHAM) to predict the multiplicity of the solutions of two …