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
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 belong to a Jordan block. Also many other conditions are derived depending upon the
choice of collocation parameters used in the solution procedure.