Stability results for collocation methods for Volterra integral equations

摘要

Stability behavior is investigated for polynomial spline collocation applied to Volterra integral equations with special emphasis on a weakly singular test equation. The characterization of the corresponding stability domain is related to stability results for solutions of finite recursion relations, as they occur for methods applied to ordinary differential equations. Estimates of the stability domains are established and, as a consequence, conditions for A(π2)-stability are obtained. Exploiting these estimates, collocation approximations with constant, linear, and continuous splines are considered in more depth and several numerical illustrations are presented.