Balanced Milstein schemes for the numerical approximation of stochastic Volterra integral equations

In this work, we present the mean square convergence and stability of balanced Milstein methods for the numerical approximation of Itô stochastic Volterra integral equations. These numerical methods comprise a family of efficient schemes that produce convergence with an order of 1.0 in the mean square. By utilizing a linear convolution test equation, we discuss the mean square stability analysis of the balanced Milstein schemes. Furthermore, numerical experiments demonstrate the convergence of these methods and compare their stability properties with the explicit Milstein scheme.