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Beyond Perturbation: Introduction to the Homotopy Analysis Method
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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 Kármán 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. less
Taylor and Francis; October 2003
336 pages; ISBN 9781135438296
Read online, or download in secure PDF format
336 pages; ISBN 9781135438296
Read online, or download in secure PDF format
Subject categories
- Academic > Mathematics > Geometry. Trigonometry.Topology > Algebraic topology
- Academic > Mathematics > Geometry. Trigonometry.Topology > Homotopy theory
- Academic > Mathematics > Tables
- Technology > Engineering > Mechanical
- Mathematics > Differential Equations
- Mathematics > Applied
- Mathematics > Probability & Statistics
- Science > Physics
ISBNs
0203491165
9780203491164
9781135438289
9781135438296
9781584884071