Sobolev gradient methods: Application to Pulse Propagation in Fiber Optics

Nauman Raza; Sultan Sial

ISBN 10: 3838385012 / ISBN 13: 9783838385013

Published by LAP LAMBERT Academic Publishing, 2010

About this Item

BRAND NEW softcover, minor shelf/handling wear.

Seller Inventory # 118120

Bibliographic Details

• Title: Sobolev gradient methods: Application to Pulse Propagation in Fiber Optics
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2010
• Language: English
• ISBN 10: 3838385012
• ISBN 13: 9783838385013
• Binding: Soft cover
• Condition: As New
• Book Type: Book

About this title

Synopsis

Sobolev gradient methods resolve numerical difficulties in approximating solutions to differential equations and minima of error and energy functionals by construction of inner product spaces that one suitable for the problem at hand. The great efficiency achieved by setting the problem in right Sobolev space, makes steepest descent methods applicable to wide variety of problems. In this monograph, applications of Sobolev gradient methods in finite-difference and finite-element settings are considered for minimization of energy functionals, soliton solutions of the nonlinear Schrodinger equation, and pulse propagation through a fiber optic cable. For each problem, the practical application of the principle of selecting an appropriate Sobolev space setting is demonstrated. The advantages of the Sobolev gradient approach in efficiency and simplicity of implementation are shown. Engineers and computational physicists will find a clear description of the numerical method allowing immediate applications to problems of their interest.

About the Author

Dr. Nauman Raza is an Assistant Professor at the University of Management and Technology. He has M.Sc. degrees in Mathematics and Telecommunications and a Ph.D. in Mathematics. His research interests are in application of Sobolev gradient methods to partial and integro-differential equations, superconductors and organic diodes.