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Unified presentation of modeling, mathematical methods, and scientific computation
Examples and exercises are included in every chapter and scientific packages such as Mathematica, Maple, and MATLAB may be easily incorporated as problem-solving tools for material presented in the work
Numerous real-world applications, including wave motion models, vehicular traffic flow, and population dynamics
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.
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.