Generalized Collocation Methods

Solutions to Nonlinear Problems

Nicola Bellomo, Bertrand Lods, Roberto Revelli , Luca Ridolfi

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English

Birkhauser Boston Inc
16 October 2007

Calculus & mathematical analysis; Maths for scientists; Maths for engineers

Series: Modeling and Simulation in Science, Engineering and Technology

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.

By: Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi
Imprint: Birkhauser Boston Inc
Country of Publication: United States
Edition: 2008 ed.
Dimensions: Height: 235mm, Width: 155mm, Spine: 16mm
Weight: 483g
ISBN: 9780817645250
ISBN 10: 081764525X
Series: Modeling and Simulation in Science, Engineering and Technology
Pages: 196
Publication Date: 16 October 2007
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Mathematical Models and Problems in Applied Sciences.- Lagrange and Sinc Collocation Interpolation Methods.- Nonlinear Initial Value Problems in Unbounded Domains.- Nonlinear Initial-Boundary Value Problems in One Space Dimension.- Initial-Boundary Value Problems in Two Space Dimensions.- Additional Mathematical Tools for Nonlinear Problems.

Reviews for Generalized Collocation Methods: Solutions to Nonlinear Problems

From the reviews: This book is concerned with the solution of initial-boundary partial differential equations using the generalised collocation method. Most of the book describes examples of how the method works for a range of examples. It is aimed primarily at engineering students. The book starts by looking at general considerations of mathematical modelling and discusses dimensional analysis. (Kenneth Wright, Mathematical Reviews, Issue 2008 g) This textbook is intended for undergraduate engineering students who wish to learn about mathematical modeling, along with the use of collocation methods for nonlinear evolutionary problems. The method of lines obtained from collocation is solved by a Mathematica routine. The book contains an appendix giving several Mathematica programs for problems . (Gerald W. Hedstrom, Zentralblatt MATH, Vol. 1135 (13), 2008) The book has been written primarily for scientists, engineers, and university students with a good knowledge of basic mathematics