Collocation Methods for Volterra Integral and Related Functional Differential Equations (Cambridge Monographs on Applied and Computational Mathematics)

This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations. It guides the reader from the "basics" to the current state-of-the-art level of the field, describes important problems and directions for future research, and highlights methods. The analysis includes numerous exercises and applications to the modelling of physical and biological phenomena.

This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations. Its principal aims are to guide the reader from basic ideas to the current state of the art, to describe important problems and directions for future research, and to highlight the benefits of the methods. The treatment is systematic and self-contained, numerous exercise are included, and applications to the mod elling of physical and biological phenomena are covered.