R-K formulae applied to Volterra equations with delay (Q753464)

The authors study Runge-Kutta methods for Volterra integral equations on a compact interval, with fixed delay. Stability is studied for convolution equations, and necessary and sufficient conditions are derived, in particular for stably stiff equations. Stable methods with reasonable orders of convergence are indicated. Numerical experiments confirming the stability and convergence properties are presented as well. These stable methods are different from those applicable to general Volterra integral equations with smooth kernel.