Stability analysis of Runge-Kutta methods for Volterra integro-differential equations

摘要

This paper is concerned with the stability properties of Runge-Kutta methods for Volterra integro-differential equations. Both the basic test equation and a convolution test equation are considered. Some fixed order recurrence relations and the corresponding stability conditions are derived for general methods. The concept of V-0-stability is introduced for the convolution test equation and some V-0-stable one-stage methods are found. The A(0)-stability and V-0-stability of the fully implicit discretized collocation methods with one or two stages are investigated in details. Finally, some numerical experiments are given to illustrate the obtained theoretical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.