Generalized Collocation Methods: Solutions to Nonlinear Problems [Hardcover]

Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a variety of mathematical problems. These include wave motion models, hydrodynamic models of vehicular traffic flow, convection-diffusion models, reaction-diffusion models, and population dynamics models. The book may be used as a textbook for graduate courses on collocation methods, nonlinear modeling, and nonlinear differential equations. Examples and exercises are included in every chapter.

Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches its subject by focusing on collocation methods for solving nonlinear evolution equations and applying them to mathematical 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.

From the reviews:

This book is concerned with the solution of initial-boundary partial differential equations using the generalised collocation method. Most of the book describes examples of how the method works for a range of examples. It is aimed primarily at engineering students. The book starts by looking at general considerations of mathematical modelling and discusses dimensional analysis. (Kenneth Wright, Mathematical Reviews, Issue 2008 g)

This textbook is intended for undergraduate engineering students who wish to learn about mathematical modeling, along with the use of collocation methods for nonlinear evolutionary problemsl3œ