Collocation Methods for Volterra Integral and Related Functional Differential Equations

ISBN-13: 9780521806152 / Angielski / Twarda / 2004 / 612 str.

Hermann Brunner; H. Brunner; M. J. Ablowitz

Opis

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.

Recenzje

'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

Spis treści

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.