Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 2, Pages 181-194
doi:10.1155/JAMSA.2005.181
Exact and approximate solutions of delay differential equations with nonlocal history conditions
Department of Mathematics, Indian Institute of Technology, Kanpur 208 016, India
Received 28 April 2004; Revised 23 July 2004
Copyright © 2005 S. Agarwal and D. Bahuguna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the exact and approximate solutions of a delay
differential equation with various types of nonlocal history
conditions. We establish the existence and uniqueness of mild,
strong, and classical solutions for a class of such problems using
the method of semidiscretization in time. We also establish a
result concerning the global existence of solutions. Finally, we
consider some examples and discuss their exact and approximate
solutions.