Loading...
Time discretization schemes for stochastic subdiffusion and fractional wave equations with integrated additive noise
Chen, Minghua Shi, Jiankang Song, Zhen Yan, Yubin Zhou, Zhi
Chen, Minghua
Shi, Jiankang
Song, Zhen
Yan, Yubin
Zhou, Zhi
Citations
Altmetric:
Advisors
Editors
Other Contributors
EPub Date
Publication Date
2025-12-04
Submitted Date
Collections
Files
Loading...
Published version
Adobe PDF, 1.61 MB
Other Titles
Abstract
In this paper, we introduce a time discretization scheme for solving the stochastic subdiffusion equation based on the two-fold integral-differential and two step backward differentiation formula (ID2-BDF2). We prove that this scheme attains a convergence rate of O ( τ α + γ − 1 / 2 ) for 1 / 2 < α + γ < 2 with α ∈ (0, 1) and γ ∈ [0, 1]. Our approach regularizes the additive noise through a two-fold integral-differential (ID2) calculus and discretizes the equation using BDF2 convolution quadrature, achieving superlinear convergence in solving the stochastic subdiffusion. Furthermore, we extend the scheme to solve the stochastic fractional wave equation, proving that the scheme achieves a convergence rate of O ( τ min { 2 , α + γ − 1 / 2 } ) for α ∈ (1, 2) and γ ∈ [0, 1]. Numerical examples are presented to validate the theoretical results for the linear problem. The numerical observations further indicate that the same convergence rates also apply to stochastic semilinear time-fractional equations.
Citation
Chen, M., Shi, J., Song, Z., Yan, Y., & Zhou, Z. (2026). Time discretization schemes for stochastic subdiffusion and fractional wave equations with integrated additive noise. Computers & Mathematics with Applications, 202, 155-169. https://doi.org/10.1016/j.camwa.2025.11.012
Publisher
Elsevier
Journal
Computers & Mathematics with Applications
Research Unit
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
Crown Copyright © 2025 Published by Elsevier Ltd.
Series/Report no.
ISSN
0898-1221
EISSN
1873-7668
ISBN
ISMN
Gov't Doc
Test Link
Sponsors
This research was supported by the Science Fund for Distinguished Young Scholars of Gansu Province under Grant No. 23JRRA1020 and National Natural Science Foundation of China under Grant No. 12471381.