Last edited by Dojind
Thursday, August 6, 2020 | History

1 edition of Homotopy Analysis Method in Nonlinear Differential Equations found in the catalog. # Homotopy Analysis Method in Nonlinear Differential Equations

## by Shijun Liao

Written in English

Subjects:
• Differential equations,
• Partial Differential equations,
• Engineering mathematics,
• Nonlinear Dynamics,
• Ordinary Differential Equations,
• Mathematics,
• Appl.Mathematics/Computational Methods of Engineering

• Edition Notes

Classifications The Physical Object Statement by Shijun Liao Contributions SpringerLink (Online service) LC Classifications QA370-380 Format [electronic resource] / Open Library OL27043916M ISBN 10 9783642251320

This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis Author: Kuppalapalle Vajravelu. Marinca et al.  made some comments on our paper  and pointed out ''some fundamental mistakes and misinterpretations along with a false conclusion'. Unfortunately, Marinca's comments are wrong. .

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence Cited by: 3. valid for weakly nonlinear ordinary differential equations (ODEs) and partial differ- ential equations (PDEs) in general. The homotopy analysis method(HAM)is an analytic approximation method for.

Description: "Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, .   AbstractIn this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat Cited by: 4.

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### Homotopy Analysis Method in Nonlinear Differential Equations by Shijun Liao Download PDF EPUB FB2

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy.

Homotopy Analysis Method in Nonlinear Differential Equations - Kindle edition by Liao, Shijun. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note Manufacturer: Springer. "Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy Brand: Springer-Verlag Berlin Heidelberg.

The governing partial differential equations are transformed into a system of nonlinear ordinary differential equations. The homotopy analysis method is used to solve the resulting coupled Author: Shijun Liao. from book Homotopy Analysis Method in Nonlinear Differential Equations (pp) Homotopy Analysis Method in Nonlinear Differential Equations Chapter January with ReadsAuthor: Shijun Liao.

The homotopy analysis method, introduced first by Liao, is a general approximate analytic approach used to obtain series solutions of nonlinear equations of various types, including algebraic equations, Cited by: In this paper, a new technique of homotopy analysis method (nHAM) is proposed for solving second order nonlinear differential equations.

This method improves the convergence of the series solution, Cited by: The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation.

Abstract. A modified -homotopy analysis method (m-HAM) was proposed for solving th-order nonlinear differential equations. This method improves the convergence of the series solution in the HAM which Cited by: 5. This book presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM).

Reviews basic concepts. Get this from a library. Homotopy analysis method in nonlinear differential equations. [Shijun Liao] -- Annotation.

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest. springer, Homotopy Analysis Method in Nonlinear Differential Equations' presents the latest developments and applications of the analytic approximation method for highly nonlinear problems.

The homotopy analysis method (HAM) [] has been proved to be one of the useful techniques to solve numerous linear and nonlinear functional equations [13–17].As mentioned in [13, 14], unlike all Cited by: 3.

where the nonlinear term is represented by F(u) and 4is the Laplace operator in Rn Here we solve these problems by homotopy analysis method and shows that homotopy perturbation method is the special File Size: KB.

Homotopy analysis method in nonlinear differential equations Shijun Liao Part I. Basic Ideas and Theorems -- Introduction -- Basic Ideas of the Homotopy Analysis Method -- Optimal Homotopy.

Homotopy Analysis Method in Nonlinear Differential Equations: : Liao, Shijun: Books. Skip to main content. Try Prime EN Hello. Sign in Account & Lists Sign in Account & Lists Returns & Orders Author: Shijun Liao. In this video, the Homotopy Perturbation Method is compared with the Numerical Method.

dsolve vs dsolve (numeric). In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion–reaction equations.

The validity of this method has been successful by applying it for these Cited by: The question refers to chapter two of the book Liao, Shijun. Homotopy analysis method in nonlinear differential equations. Beijing: Higher Education Press, Link to book pdf from site (presumably author related).

In section of the book. Approximate Solutions of Nonlinear Partial Differential Equations by Modified -Homotopy Analysis Method 1 2 Mathematics Department, Faculty of Computer Science and. S.T. Mohyud-Din and M.A. Noor The HPM for Solving Partial Differential Equations this reliable technique for solving PDEs.

In particular the proposed homotopy perturbation method (HPM) is tested. In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations.

The method has been successively provided for finding Cited by: like homotopy analysis transform method. The proposed method is coupling of the homotopy analysis method HAM and Laplace transform method [].

We have studied some of linear and nonlinear Author: M.S. Mohamed, M.R. Alharthi, R.A. Alotabi.
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