Error analysis of a fully discrete method for time-fractional diffusion equations with a tempered fractional Gaussian noise

Liu, Xing

doi:10.1016/j.cam.2024.115953

Journal of Computational and Applied Mathematics

2024

DOI: 10.1016/j.cam.2024.115953

|View full text |Cite

Error analysis of a fully discrete method for time-fractional diffusion equations with a tempered fractional Gaussian noise

Xing Liu

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise

Wu,

Yan

2024

Mathematics

View full text Add to dashboard Cite

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.

show abstract

Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise

Wu,

Yan

2024

Mathematics

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Error analysis of a fully discrete method for time-fractional diffusion equations with a tempered fractional Gaussian noise

Cited by 1 publication

References 28 publications

Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise

Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise

Contact Info

Product

Resources

About