Numerical Methods for Delay Differential Equations [Hardcover]

The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising behaviors of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods.

1. Introduction
2. Existence and regularity of solutions of DDEs
3. A review of DDE methods
4. The standard approach via continuous ODE methods
5. Continuous Runge-Kutta methods for ODEs
6. Runge-Kutta methods for DDEs
7. Local error estimation and variable stepsize
8. Stability analysis of Runge-Kutta methods for ODEs
9. Stability analysis of DDEs
10. Stability analysis of Runge-Kutta methods for DDEs

...this is a serious monograph...It will serve as a guide and a reference for researchers and engineers interested in numerical solution of models from real-life applications. It may also serve as a textbook for a graduate-level course in this area that may be offered at some universities. --SIAMReview