Strong convergence order for the scheme of fractional diffusion equation driven by fractional Gaussion noise

by   Daxin Nie, et al.

Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index H>1/2, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving stochastic fractional diffusion equation driven by fractional Gaussian noise. Using the operator theoretical approach, we present the regularity estimate of the mild solution and the fully discrete scheme with finite element approximation in space and backward Euler convolution quadrature in time. The 𝒪(τ^H-ρα) convergence rate in time and 𝒪(h^min(2,2-2ρ,H/α)) in space are obtained, showing the relationship between the regularity of noise and convergence rates, where ρ is a parameter to measure the regularity of noise and α∈(0,1). Finally, numerical experiments are performed to support the theoretical results.


page 1

page 2

page 3

page 4

∙ 01/06/2021

Numerical analysis for stochastic time-space fractional diffusion equation driven by fractional Gaussion noise

In this paper, we consider the strong convergence of the time-space frac...
∙ 01/26/2022

Numerical Approximation for Stochastic Nonlinear Fractional Diffusion Equation Driven by Rough Noise

In this work, we are interested in building the fully discrete scheme fo...
∙ 04/28/2021

A unified convergence analysis for the fractional diffusion equation driven by fractional Gaussion noise with Hurst index H∈(0,1)

Here, we provide a unified framework for numerical analysis of stochasti...
∙ 12/10/2021

Regularity theory and numerical algorithm for the fractional Klein-Kramers equation

Fractional Klein-Kramers equation can well describe subdiffusion in phas...
∙ 08/16/2021

A Numerical Method for a Nonlocal Diffusion Equation with Additive Noise

We consider a nonlocal evolution equation representing the continuum lim...
∙ 10/12/2019

Numerical algorithm for the model describing anomalous diffusion in expanding media

We provide a numerical algorithm for the model characterizing anomalous ...
∙ 11/25/2022

Generalized convolution quadrature for the fractional integral and fractional diffusion equations

We consider the application of the generalized Convolution Quadrature (g...

Please sign up or login with your details

Forgot password? Click here to reset