Beyond Perturbation: Introduction to the Homotopy Analysis Method

Abstract

9R2. Beyond Perturbation: Introduction to the Homotopy Analysis Method. - Edited by Shijun Liao (Shanghai Jiao Tong University, Shanghai, China). Chapman and Hall/CRC Press, Boca Raton FL. 2004. 322 pp. ISBN 1-58488-407-X.Reviewed by SA Sherif (Dept of Mech and Aerospace Eng, Univ of Florida, 232 MAE Bldg B, PO Box 116300, Gainesville FL 32611-6300).This book deals with a very interesting mathematical technique that is rather powerful. While perturbation methods work nicely for slightly nonlinear problems, the homotopy analysis technique addresses nonlinear problems in a more general manner. Through this method, the author demonstrates that a nonlinear problem that normally has a unique solution can have an infinite number of different solution expressions whose convergence region and rate