This book examines various mathematical toolsa "based on
generalized collocation methodsa "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 MathematicaA(R), readers
may use other packages such as MATLABA(R) 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.
General
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