MEAN SQUARE STABILITY OF NUMERICAL METHOD FOR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH DOUBLE WEAKLY SINGULAR KERNELS

Rouz O. F., Shahmorad S., Erdoğan F.

International Journal of Numerical Analysis and Modeling, cilt.22, sa.6, ss.755-776, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.4208/ijnam2025-1033
  • Dergi Adı: International Journal of Numerical Analysis and Modeling
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.755-776
  • Anahtar Kelimeler: mean square stability, SOE approximation, Stochastic Volterra integral equations, stochastic θ-scheme, weakly singular kernels
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

The main goal of this paper is to develop an improved stochastic θ-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 pa-rameters. To overcome the low computational efficiency of the stochastic θ-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 θ-method and the θ-Milstein method. The results confirm that our approach aligns significantly with the expected physical interpretations.