Collocation Methods for Volterra Integral and Related Functional Differential Equations

An introduction for graduate students, a guide for users, and a comprehensive resource for experts.

Hermann Brunner (Author)

9780521806152, Cambridge University Press

Hardback, published 15 November 2004

612 pages, 70 b/w illus. 158 exercises
23.6 x 15.8 x 4 cm, 1.384 kg

'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

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.

1. The collocation method for ODEs: an introduction
2. Volterra integral equations with smooth kernels
3. Volterra integro-differential equations with smooth kernels
4. Initial-value problems with non-vanishing delays
5. Initial-value problems with proportional (vanishing) delays
6. Volterra integral equations with weakly singular kernels
7. VIDEs with weakly singular kernels
8. Outlook: integral-algebraic equations and beyond
9. Epilogue.

Subject Areas: Numerical analysis [PBKS]