Generalized Collocation Methods: Solutions to Nonlinear Problems

Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi9780817645250, 081764525X, 0817646108

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 MathematicaÂR, readers may use other packages such as MATLABÂR or MapleTM depending on their specific needs and software preferences.