Collocation Methods for Volterra Integral and Related Functional Differential
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;
An introduction for graduate students, a guide for users, and a comprehensive resource for experts.