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

Synopsis

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. 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. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. 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.

Copyright:

2003

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9781135438289

Related ISBNs:

9781135438296, 9781135438241, 9781584884071, 9780429208614

Publisher:

CRC Press

Date of Addition:

12/06/24

Copyrighted By:

Taylor & Francis Group, LLC

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Technology, Earth Sciences, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.