This chapter introduces the classes of DDEs and neutral DDEs treated in the book, focusing on some of the most significant qualitative differences between delay equations and ordinary equations, as well as on how such differences reflect in their numerical treatment. Some examples are given that stress the different behaviours of the solutions, either in terms of existence and uniqueness in dependence of the initial data, or in terms of the asymptotic behaviour in dependence of the parameters of the considered test problems. Evidence is given that integration of DDEs cannot be based on the mere adaptation of some standard ODE code to the presence of delayed terms. Integration of DDEs requires the use of specifically designed methods according to the nature of the equation and the behaviour of the solution.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.