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Generalized Collocation Methods

Solutions to Nonlinear Problems

  • Nicola Bellomo
  • Bertrand Lods
  • Roberto Revelli
  • Luca Ridolfi

Table of contents

  1. Front Matter
    Pages I-XII
  2. Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
    Pages 1-32
  3. Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
    Pages 33-56
  4. Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
    Pages 57-76
  5. Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
    Pages 77-102
  6. Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
    Pages 103-126
  7. Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
    Pages 127-164
  8. Back Matter
    Pages 165-194

About this book

Introduction

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 MapleTM 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.

Keywords

Boundary value problem MATLAB Maple analysis collocation methods convection-diffusion models differential quadrature method hydrodynamic models modeling nonlinear evolution equations operator population dynamics reaction-diffusion models tran wave phenomena models

Editors and affiliations

  • Nicola Bellomo
    • 1
  • Bertrand Lods
    • 2
  • Roberto Revelli
    • 3
  • Luca Ridolfi
    • 4
  1. 1.Dipartimento di MatematicaPolitecnico di Torino10129 TorinoItalia
  2. 2.Laboratoire de Mathématiques Université Blaise PascalCampus Universitaire des Cézeaux 63177 Aubiere cedexFrance
  3. 3.Dipartimento di Idraulica, Trasporti, ed Infrastrutture CiviliPolitecnico di Torino Corso Duca degli Abruzzi 2410129 TorinoItalia
  4. 4.Dipartimento di Idraulica, Trasporti, ed Infrastrutture CiviliPolitecnico di Torino Corso Duca degli Abruzzi 2410129 TorinoItalia

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4610-3
  • Copyright Information Springer 2008
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4525-0
  • Online ISBN 978-0-8176-4610-3
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • Buy this book on publisher's site