An optimal homotopy-analysis approach for strongly nonlinear differential equations

S Liao - Communications in Nonlinear Science and Numerical …, 2010 - Elsevier
In this paper, an optimal homotopy-analysis approach is described by means of the
nonlinear Blasius equation as an example. This optimal approach contains at most three …

Notes on the homotopy analysis method: some definitions and theorems

S Liao - Communications in Nonlinear Science and Numerical …, 2009 - Elsevier
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 …

Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet

M Sajid, T Hayat - International Communications in Heat and Mass …, 2008 - Elsevier
The effect of radiation on the boundary layer flow and heat transfer of a viscous fluid over an
exponentially stretching sheet is studied. The homotopy analysis method (HAM) is employed …

A general approach to obtain series solutions of nonlinear differential equations

S Liao, Y Tan - Studies in Applied Mathematics, 2007 - Wiley Online Library
Based on homotopy, which is a basic concept in topology, a general analytic method
(namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear …

The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation

S Abbasbandy - Physics Letters A, 2007 - Elsevier
Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to
solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to …

[HTML][HTML] Analytically pricing double barrier options based on a time-fractional Black–Scholes equation

W Chen, X Xu, SP Zhu - Computers & Mathematics with Applications, 2015 - Elsevier
This paper investigates the pricing of double barrier options when the price change of the
underlying is considered as a fractal transmission system. In this scenario, the option price is …

MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface

T Hayat, T Javed, Z Abbas - Nonlinear Analysis: Real World Applications, 2009 - Elsevier
The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an
incompressible micropolar fluid over a non-linear stretching surface is studied. The resulting …

MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface

T Hayat, Z Abbas, M Sajid - Chaos, Solitons & Fractals, 2009 - Elsevier
The present analysis comprises the steady two-dimensional magnetohydrodynamic flow of
an upper-convected Maxwell fluid near a stagnation-point over a stretching surface. The …

Series solutions of non-linear Riccati differential equations with fractional order

J Cang, Y Tan, H Xu, SJ Liao - Chaos, Solitons & Fractals, 2009 - Elsevier
In this paper, based on the homotopy analysis method (HAM), a new analytic technique is
proposed to solve non-linear Riccati differential equation with fractional order. Different from …

A general approach to get series solution of non-similarity boundary-layer flows

SJ Liao - Communications in Nonlinear Science and Numerical …, 2009 - Elsevier
An analytic method for strongly non-linear problems, namely the homotopy analysis method
(HAM), is applied to give convergent series solution of non-similarity boundary-layer flows …