Beyond Perturbation

Introduction to the Homotopy Analysis Method
1. Auflage 2003
ISBN: 978-1-58488-407-1
Verlag: CRC Press

Buch, Englisch, 334 Seiten, Format (B × H): 157 mm x 247 mm, Gewicht: 630 g

Reihe: Modern Mechanics and Mathematics

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.

Zielgruppe

Professional

Autoren/Hrsg.

Liao, Shijun

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

PART I BASIC IDEAS: Introduction. Illustrative Description. Systematic Description. Relations to Some Previous Analytic Methods. Advantages, Limitations, and Open Questions. PART II APPLICATIONS: Simple Bifurcation of a Nonlinear Problem. Multiple Solutions of a Nonlinear Problem. Nonlinear Eigenvalue Problem. Thomas-Fermi Atom Model. Volterra's Population Model. Free Oscillation Systems with Odd Nonlinearity. Free Oscillation Systems with Quadratic Nonlinearity. Limit Cycle in a Multidimensional System. Blasius' Viscous Flow. Boundary-layer Flow with Exponential Property. Boundary-layer Flow with Algebraic Property. Von Kármán Swirling Flow. Nonlinear Progressive Waves in Deep Water. BIBLIOGRAPHY. INDEX

Über Autor(innen)

Shijun Liao (Shanghai Jiao Tong University, Shanghai, China)