MITTAG-LEFFLER EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

This paper reconsiders the linear stochastic Volterra integral equations with weakly singular kernels. For the equivalent form of the underlying equation, we propose the improved version of the existing mean-square asymptotical stability result for the exact solution. Moreover, some new or improved results are obtained for the Mittag-Leffler Euler–Maruyama method for the equations, and it is shown that the method shares sharp strong convergence with order $ 1/2-\beta $ and carries preferable stability. The numerical examples are performed to show the accuracy and effectiveness of the numerical scheme and verify the correctness of the theoretical analysis.