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Numerical approximation of semilinear stochastic subdiffusion driven by fractionally integrated fBm via the Mittag-Leffler Euler scheme
Li, Zhiqiang Yan, Yubin
Li, Zhiqiang
Yan, Yubin
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2026-01-05
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This paper introduces a numerical method for solving the stochastic semilinear subdiffusion equation with fractionally integrated additive fractional Brownian motion (fBm). The temporal discretization is carried out using the Mittag-Leffler Euler method, while the spatial variable is approximated by the spectral Galerkin method. We prove that the resulting fully discrete scheme attains the optimal strong convergence rate O ( τ min { α , H + α + γ − 1 } ) for all H ∈ (0, 1), thereby overcoming the 1/2-order restriction reported in [1]. Here, τ denotes the time step size, H ∈ (0, 1) is the Hurst parameter, α ∈ (0, 1) is the order of the Caputo fractional derivative, and γ ∈ [0, 1] is the order of the Riemann-Liouville fractional integral. Numerical experiments are presented to demonstrate the accuracy of the method and to confirm the sharpness of the theoretical convergence results.
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Li, Z., & Yan, Y., (2026). Numerical approximation of semilinear stochastic subdiffusion driven by fractionally integrated fBm via the Mittag-Leffler Euler scheme. Communications in Nonlinear Science and Numerical Simulation, 156, 109633. https://doi.org/10.1016/j.cnsns.2025.109633
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Elsevier
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Communications in Nonlinear Science and Numerical Simulation
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Article
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en
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© 2025 The Author(s). Published by Elsevier B.V.
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1007-5704
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1878-7274
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This work was partially supported by the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2025L130) and the Shanxi Scholarship Council of China (No. 2024-139).