This book examines various mathematical tools--based on generalized collocation methods--to solve nonlinear problems related to partial differential and integrodifferential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convention and diffusion, transport phenomena, and pollution.
The volume is written for an interdisciplinary audience: graduate students, engineers, scientists, and applied mathematicians interested in modeling real-world systems by differential or operator equations. It 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. Contents
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 | Appendix: Scientific Programs Related Topics
Applied Mathematics, Calculus and Analysis, Differential Equations, Engineering, Physics