TY - JOUR
T1 - Mean Square Stability of Numerical Method for Stochastic Volterra Integral Equations with Double Weakly Singular Kernels
AU - Rouz , Omid Farkhondeh
AU - Shahmorad , Sedaghat
AU - Erdogan , Fevzi
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 755
EP - 776
PY - 2025
DA - 2025/08
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1033
UR - https://global-sci.org/intro/article_detail/ijnam/24292.html
KW - Stochastic Volterra integral equations, weakly singular kernels, stochastic $θ$-scheme, SOE approximation, mean square stability.
AB - <p style="text-align: justify;">The main goal of this paper is to develop an improved stochastic $\theta$-scheme as a numerical method for stochastic Volterra integral equations (SVIEs) with double weakly singular
kernels and demonstrate that the stability of the proposed scheme is affected by the kernel parameters. To overcome the low computational efficiency of the stochastic $\theta$-scheme, we employed
the sum-of-exponentials (SOE) approximation. Then, the mean square stability of the proposed
scheme with respect to a convolution test equation is studied. Additionally, based on the stability
conditions and the explicit structure of the stability matrices, analytical and numerical stability
regions are plotted and compared with the split-step $\theta$-method and the $\theta$-Milstein method. The
results confirm that our approach aligns significantly with the expected physical interpretations.</p>