Stability of Collocation Methods for Volterra Integro-Differential Equations

Abstract

We investigate the stability properties of exact and discretized collocation methods, with respect to Volterra integro-differential equations, with degenerate kernel and the basic test equation.

Stability for a class of difference equations

“…Theorem 2.2 and Remark 2.2 will be useful to obtain sufficient condition that the zero solution of (1.1) is uniformly asymptotically stable (cf. [1][2][3][4][5]10,15,16,19,20]). Finally in this section, under the condition…”

“…Using the Liapunov technique, Crisci et al [1][2][3] and Vecchio [19,20] have analyzed the various stability of numerical methods. They are, for example, the first-order and some higher order backward differential formulas, and the implicit Euler methods without requiring the summability of the kernel.…”