International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1049-1066
doi:10.1155/IJMMS.2005.1049
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
Abstract
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.