The stability of collocation methods for VIDEs of second order - Edris Rawashdeh; Dave McDowell; Leela Rakesh (International Journal of Mathematics and Mathematical Sciences)
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.