New Trends in Perturbation Methods with Applications

This book discusses perturbation methods for solving algebraic and differential equations. The basics of the methods and the classical results are discussed in detail. Recent developments in the methods for solving algebraic and differential equations are also included. Classical perturbation methods depend on the smallness of a perturbation parameter for which the solutions are not valid for large parameters. Recent methods to increase the range of validity of perturbation solutions are given in the book. The new methods produce valid solutions for strongly nonlinear systems in addition to weakly nonlinear systems. The book will be beneficial for applied mathematicians, engineers, and physicists who are in search of approximate solutions for their specific problems. It can be adopted as a graduate textbook for courses on perturbation methods.