E-raamat: Approximate Analytical Methods for Solving Ordinary Differential Equations

The textbook works through some important approximate methods for solving ordinary differential equations and provides a number of illustrations from several fields such as biology, physics, and economics. It considers both well established techniques and some recently developed procedures, along with detailed examples of how to apply the methods to solve real-world problems. Readers should be comfortable with advanced calculus and have taken an elementary course on differential equations. The topics are the power series method, the asymptotic method, perturbation techniques, the method of multiple scales, WKB (Wentzel, Kramers, Brillown) theory, non-perturbation methods, and homotopy methods. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.

The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete description of the methods without going deep into rigorous mathematical aspects. Detailed examples illustrate the application of the methods to solve real-world problems.

The authors introduce the classical power series method for solving differential equations before moving on to asymptotic methods. They next show how perturbation methods are used to understand physical phenomena whose mathematical formulation involves a perturbation parameter and explain how the multiple-scale technique solves problems whose solution cannot be completely described on a single timescale. They then describe the Wentzel, Kramers, and Brillown (WKB) method that helps solve both problems that oscillate rapidly and problems that have a sudden change in the behavior of the solution function at a point in the interval. The book concludes with recent nonperturbation methods that provide solutions to a much wider class of problems and recent analytical methods based on the concept of homotopy of topology.