Perturbation Methods For Differential Equations

Many differential equations with nonlinearities or variable coefficients do not permit the construction of exact solutions. This book introduces several perturbation methods that can be used to develop approximate solutions of such equations. To accommodate an interdisciplinary readership, the author focuses almost exclusively on procedures, underlying ideas and applications, and minimizes technical proofs.

The book begins with an introduction to the idea of asymptotic approximations to the evaluation of transcendental functions and the solution of differential equations, as well as a discussion of the regular perturbation approach. What follows is a systematic and unified treatment of the resolution of the nonuniformities produced, as a rule, by the regular perturbation method. Several singular perturbation methods are examined, including the methods of: strained parameters, averaging, matched asymptotic expansions, multiple scales, and quantum-field-theoretic renormalization.

Methods treated are applied to ordinary and partial differential equations arising in various problems of solid mechanics, fluid dynamics, and plasma physics. Background material is provided in each chapter along with illustrative examples, problems, and selected solutions. A comprehensive bibliography and index complete the work.

Perturbation Methods for Differential Equations serves as a textbook for graduate students and advanced undergraduate students in applied mathematics, physics, and engineering who want to enhance their expertise with mathematical methods via a one- or two-semester course. Researchers in these areas will also find the book an excellent reference.