International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 19, Pages 3075-3089
doi:10.1155/IJMMS.2005.3075
The stability of collocation methods for higher-order Volterra integro-differential equations
Department of Mathematics, Center for Applied Mathematics and Polymer Fluid Dynamics, Central Michigan University, Mt. Pleasant 48859, MI, USA
Received 20 December 2004; Revised 17 July 2005
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.
Abstract
The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the new method are given and the efficiency of the new method is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-order integro-differential equations.