Manual Beyond Perturbation: Introduction to the Homotopy Analysis Method (Modern Mechanics and Mathematics)

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Description Table of Contents Reviews. Features Presents a systematic description of homotopy analysis-a new method for nonlinear problems Describes a convergence theorem for general cases and shows that other techniques, such as the d -expansion method, Lyapunov's artificial small parameter method, and Adomian's decomposition method, are only special cases of the homotopy analysis method Discusses the method's advantages, limitations, and related open questions Illustrates the use of homotopy analysis in many interesting problems, which makes the formulations, theories, and applications easy to follow Summary Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become.

Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity.

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In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages and limitations of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form.

Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open. Reviews "The author has invested a great amount of effort into determining all the power series and computing the functions depicted in the figures. I highly recommend that it be acquired by interested individuals and libraries throughout.


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