Generalized Collocation Methods [electronic resource] : Solutions to Nonlinear Problems / edited by Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi.
Contributor(s): Bellomo, Nicola [editor.] | Lods, Bertrand [editor.] | Revelli, Roberto [editor.] | Ridolfi, Luca [editor.] | SpringerLink (Online service)Material type: TextSeries: Modeling and Simulation In Science, Engineering and Technology: Publisher: Boston, MA : Birkhäuser Boston, 2008Description: XII, 196 p. 62 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817646103Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Differential equations | Applied mathematics | Engineering mathematics | Computer mathematics | Mathematical models | Mathematics | Analysis | Appl.Mathematics/Computational Methods of Engineering | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Computational Science and Engineering | Ordinary Differential EquationsAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access online
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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.
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.