Collocation Methods for Volterra Integral and Related Functional Differential Equations: 15 (Cambridge Monographs on Applied and Computational Mathematics, Series Number 15) - Hardcover

Brunner, Hermann

Hardcover

ISBN 10: 0521806151 ISBN 13: 9780521806152

Publisher: Cambridge University Press, 2004

Synopsis

Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.

About this title

Review

'The clarity of the exposition, the completeness in the presentation of stated and proved theorems, and the inclusion of a long list of exercises and open problems, along with a wide and exhaustive annotated bibliography, make this monograph a useful and valuable reference book for a wide range of scientists and engineers. In particular, it can be recommended to advanced undergraduate and graduate students in mathematics and may also serve as a source of topics for MSc. and PhD. theses in this field.' Alfredo Bellen, Universita' di Trieste

Book Description

The first comprehensive guide to the analysis of collocation methods for a wide class of initial-value problems, including equations with delay arguments. It describes important problems and directions for future research. Also includes numerous exercises, a vast bibliography with historical commentary, and important applications to modelling biological and physical phenomena.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2004
• Language: English
• ISBN 10: 0521806151
• ISBN 13: 9780521806152
• Binding: Hardcover
• Number of pages: 612