Beyond Perturbations: An Introduction to Homotopy Analysis Methods

Author: Liao Shijun
Publisher:
Publish Date: 2006-06-02
Features: As is well known, nonlinear problems are quite difficult to solve. The stronger the nonlinearity, the harder they are to solve. The perturbation expansion method provides perturbative analytical approximations, which are usually only applicable to weakly nonlinear problems. When nonlinearity increases, perturbative solutions often become invalid. This academic monograph systematically introduces a general method for solving nonlinear problems originally proposed by Professor Liao Shijun, namely the "Homotopy Analysis Method," describing the complete framework of the theoretical system, and elaborating in detail the basic ideas, criteria, proof of theorems, and the relationship and connection with other methods. The "Homotopy Analysis Method" completely discards the "small parameter assumption" widely adopted by the engineering community in the current "perturbation method" (including the "singular perturbation method"), fundamentally overcoming the strong dependence on small parameters and overcoming the limitations of the "perturbation method"