L1 scheme for semilinear stochastic subdiffusion with integrated fractional Gaussian noise

This paper considers a numerical method for solving the stochastic semilinear subdiffusion equation which is driven by integrated fractional Gaussian noise and the Hurst parameter H∈(1/2,1). The finite element method is employed for spatial discretization, while the L1 scheme and Lubich’s first-order convolution quadrature formula are used to approximate the Caputo time-fractional derivative of order α∈(0,1) and the Riemann–Liouville time-fractional integral of order γ∈(0,1), respectively. Using the semigroup approach, we establish the temporal and spatial regularity of the mild solution to the problem. The fully discrete solution is expressed as a convolution of a piecewise constant function with the inverse Laplace transform of a resolvent-related function. Based on the Laplace transform method and resolvent estimates, we prove that the proposed numerical scheme has the optimal convergence order O(τmin{H+α+γ−1−ε,α}),ε>0. Numerical experiments are presented to validate these theoretical convergence orders and demonstrate the effectiveness of this method.

Citation

Wu, X., & Yan, Y. (2025). L1 scheme for semilinear stochastic subdiffusion with integrated fractional Gaussian noise. Fractal and Fractional, 9(3), article-number 173. https://doi.org/10.3390/fractalfract9030173

Publisher

MDPI

Journal

Fractal and Fractional

URI

http://hdl.handle.net/10034/629317

DOI

10.3390/fractalfract9030173

Type

Article

Language

en

Description

© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

EISSN

2504-3110

Additional Links

https://www.mdpi.com/2504-3110/9/3/173