International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1049-1066

The stability of collocation methods for VIDEs of second order

Edris Rawashdeh, Dave McDowell, and Leela Rakesh

Department of Mathematics, Center for Applied Mathematics and Polymer Fluid Dynamics, Central Michigan University, Mount Pleasant 48859, MI, USA

Received 8 August 2004; Revised 29 December 2004

Copyright © 2005 Edris Rawashdeh et al. 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.


Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integro differential equation (VIDE) by polynomial spline functions. The polynomial spline collocation method is stable if all eigenvalues of a matrix are in the unit disk and all eigenvalues with |λ|=1 belong to a 1×1 Jordan block. Also many other conditions are derived depending upon the choice of collocation parameters used in the solution procedure.