Advances in the Homotopy Analysis Method by Shijun Liao

By Shijun Liao

Not like different analytic recommendations, the Homotopy research approach (HAM) is self sufficient of small/large actual parameters. along with, it offers nice freedom to decide on equation kind and resolution expression of comparable linear high-order approximation equations. The HAM offers an easy option to warrantly the convergence of answer sequence. Such area of expertise differentiates the HAM from all different analytic approximation tools. moreover, the HAM might be utilized to resolve a few difficult issues of excessive nonlinearity.

This ebook, edited by way of the pioneer and founding father of the HAM, describes the present advances of this strong analytic approximation process for hugely nonlinear difficulties. Coming from diverse international locations and fields of analysis, the authors of every bankruptcy are best specialists within the HAM and its functions.

Readership: Graduate scholars and researchers in utilized arithmetic, physics, nonlinear mechanics, engineering and finance.

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36 37 38 39 40 48 54 55 60 66 71 79 81 October 24, 2013 10:44 36 World Scientific Review Volume - 9in x 6in Advances/Chap. 2 S. Abbasbandy and E. 1. Preliminaries Many of the mathematical modeling of the physical phenomena in science and engineering often lead to nonlinear differential equations. There are a lot of methods, from the past up to now, to give numerically approximate solutions of nonlinear differential equations such as Euler method, RungeKutta method, multistep method, Taylor series method, Hybrid methods, family of finite difference methods [1, 2], family of finite element methods [3], meshless methods, differential quadrature, spectral methods [4–6] etc.

30] S. Abbasbandy and E. Shivanian, Predictor homotopy analysis method and its application to some nonlinear problems, Commun. Nonlinear Sci. Numer. Simulat. 16: 2456–2468 (2011). J. Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. Heat Mass Tran. 48: 2529–2539 (2005). J. Liao and E. Magyari, Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones, Z. angew. Math. Phys. 57, 777–792 (2006). J. Liao, On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves, Commun.

Nonlinear Sci. Numer. Simulat. 15: 3830–3846 (2010). [30] S. Abbasbandy and E. Shivanian, Predictor homotopy analysis method and its application to some nonlinear problems, Commun. Nonlinear Sci. Numer. Simulat. 16: 2456–2468 (2011). J. Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. Heat Mass Tran. 48: 2529–2539 (2005). J. Liao and E. Magyari, Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones, Z.

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