A two-parameter Milstein method for stochastic Volterra integral equations

Abstract In this paper, a two-parameter Milstein method for stochastic Volterra integral equations is introduced. First, the method is proved to be strongly convergent with order one in  L p norm ( p ≥ 1 ). Then, we investigate the mean square stability of the exact and numerical solutions of a stochastic convolution test equation. Stability conditions are derived. Based on these conditions, analytical and numerical stability regions are plotted and compared with each other. The results show that additional implicitness offers benefits for numerical stability. Finally, some numerical experiments are carried out to confirm the theoretical results.