STABILITY RESULTS FOR COLLOCATION METHODS FOR VOLTERRA INTEGRAL-EQUATIONS

Stability behavior is investigated for polynomial spline collocation a pplied to Volterra integral equations with special emphasis on a weakl y singular test equation. The characterization of the corresponding st ability domain is related to stability results for solutions of finite recursion relations, as they occur for methods applied to ordinary di fferential equations. Estimates of the stability domains are establish ed and, as a consequence, conditions for A(pi/2)-stability are obtaine d. Exploiting these estimates, collocation approximations with constan t, linear, and continuous splines are considered in more depth and sev eral numerical illustrations are presented.