Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise
Year: 2024
Type: article
Abstract: We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter H∈(0,1). The covariance operator Q of the stochastic fractional Wiener process satisfies ∥A−ρQ1/2∥HS < ∞ for some ρ∈[0,1), where ∥·∥HS denotes the Hilbert–Schmidt norm. The Caputo fractional derivative and Riemann–Liouville fractional integral are approximated using Lubich’s convolution quadrature formulas, while the noise is discretized via the Euler method. For the spatial derivative, we use the spectral Galerkin method. The approximate solution of the fully discrete scheme is represented as a convolution between a piecewise constant function and the inverse Laplace transform of a resolvent-related function. By using this convolution-based representation and applying the Burkholder–Davis–Gundy inequality for fractional Gaussian noise, we derive the optimal convergence rates for the proposed fully discrete scheme. Numerical experiments confirm that the computed results are consistent with the theoretical findings.
Source: Mathematics
DOI: 10.3390/math12223579
Authors: Xiaolei Wu, Yubin Yan
Institutions: Luliang University, University of Chester
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4404486474