T.S.L Radhika, T. K.V. Iyengar, T. Raja Rani
Chapman and Hall/CRC
Published November 21, 2014
Reference - 200 Pages - 31 B/W Illustrations
ISBN 9781466588158 - CAT# K20370
For Instructors Request Inspection Copy
For Librarians Available on Taylor & Francis eBooks >>
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.
Power Series Method
Algebraic Method (Method of Undetermined Coefficients)
Solution at Ordinary Point of an Ordinary Differential Equation
Solution at a Singular Point (Regular) of an Ordinary
Remarks on the Frobenius Solution at Irregular Singular Points
Taylor Series Method
Asymptotic Solutions at Irregular Singular Points at Infinity
Asymptotic Solutions of Perturbed Problems
Solutions to ODEs Containing a Large Parameter
Regular Perturbation Theory
Singular Perturbation Theory
Method of Multiple Scales
Method of Multiple Scales
WKB Approximation for Unperturbed Problems
WKB Approximation for Perturbed Problems
Lyapunov’s Artificial Small-Parameter Method
Delta Expansion Method
Adomian Decomposition Method
Homotopy Analysis Method
Homotopy Perturbation Method
Optimal Homotopy Analysis Method
Exercise Problems, Applications, and a Bibliography appear at the end of each chapter.