Keller-Box Method and Its Application

Most of the problems arising in science and engineering are nonlinear. They are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems, and often break down for problems with strong nonlinearity. This book presents the current theoretical developments and applications of the Keller-box method to nonlinear problems. The first half of the book addresses basic concepts to understand the theoretical framework for the method. In the second half of the book, the authors give a number of examples of coupled nonlinear problems that have been solved by means of the Keller-box method. The particular area of focus is on fluid flow problems governed by nonlinear equation.

Auteur

Kuppalapalle Vajravelu, University of Central Florida, Orlando, USA; Kerehalli V. Prasad, Bangalore University, India.

Résumé

"The book is a very nice exposition of an important set of results and applications. It is exceptionally well organized and one can learn many useful techniques based on finite difference methods to approximate the solutions in a broad spectrum of problems. The book is a nice choice for part of a graduate numerical course coordinated with a course on linear partial differential equations. At the same time, the book provides a suitable framework for researchers in the area." Mathematical Reviews

"In the reviewer's opinion, this book provides a fundamental and comprehensive presentation of mathematical principles of the Keller-box method and its applications to numerical solutions of problems of practical interest. The references included in this book are very important, especially for young researchers who wish to deal with numerical methods for fluid dynamics and heat transfer. Moreover, Chapter 6 provides a solid background for future research in the newer field of nanofluids. The book is very well written and readable. Results of the numerical solutions of the considered problems are given graphically and in tabular form. The book will be of interest to a wide range of specialists working in different areas of fluid mechanics and heat transfer, such as graduate, MSc and PhD students, engineers, physicists, chemical engineers, and also to researchers interested in the mathematical theory of fluid mechanics and in connected topics." Zentralblatt für Mathematik

Contenu
Chapter 1: Introduction Part I: Theoretical considerationsChapter 2: Principles of Implicit Keller-Box MethodChapter 3: Stability and convergence of Implicit Keller-Box method Part II: Application to physical problemsChapter 4: Application of Keller-Box method to fluid flow and heat transfer problemsChapter 5: Application of Keller-Box method to coupled nonlinear boundary value problemsChapter 6: Application of Keller-Box method to more advanced problems Subject IndexAuthor Index