Generalized Collocation Methods : Solutions to Nonlinear Problems

Bellomo, Nicola; Lods, Bertrand; Revelli, Roberto; Ridolfi, Luca

ISBN 10: 081764525X / ISBN 13: 9780817645250

Editore: Birkhäuser, 2007

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Dati bibliografici

• Titolo: Generalized Collocation Methods : Solutions to Nonlinear Problems
• Editore: Birkhäuser
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 081764525X
• ISBN 13: 9780817645250
• Rilegatura: Rilegato
• Condizione: New

Descrizione articolo

Riassunto

Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a variety of mathematical problems. These include wave motion models, hydrodynamic models of vehicular traffic flow, convection-diffusion models, reaction-diffusion models, and population dynamics models. The book may be used as a textbook for graduate courses on collocation methods, nonlinear modeling, and nonlinear differential equations. Examples and exercises are included in every chapter.

Dalla quarta di copertina

This book examines various mathematical tools based on generalized collocation methods to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and pollution.

Based on a unified approach combining modeling, mathematical methods, and scientific computation, each chapter begins with several examples and problems solved by computational methods; full details of the solution techniques used are given. The last section of each chapter provides problems and exercises giving readers the opportunity to practice using the mathematical tools already presented. Rounding out the work is an appendix consisting of scientific programs in which readers may find practical guidelines for the efficient application of the collocation methods used in the book. Although the authors make use of Mathematica^®, readers may use other packages such as MATLAB^® or Maple^TM depending on their specific needs and software preferences.

Generalized Collocation Methods is written for an interdisciplinary audience of graduate students, engineers, scientists, and applied mathematicians with an interest in modeling real-world systems by differential or operator equations. The work may be used as a supplementary textbook in graduate courses on modeling and nonlinear differential equations, or as a self-study handbook for researchers and practitioners wishing to expand their knowledge of practical solution techniques for nonlinear problems.