Work

Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise

Year: 2024

Type: article

Abstract: In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters H1, … , Hd+1 ∈ (0, ½] and d = 1, 2. We first provide the regularity of the solution. Then we employ the Wong–Zakai approximation to regularize the rough noise and discuss the convergence of the approximation. Next, the finite element and backward Euler convolution quadrature methods are used to discretize spatial and temporal operators for the obtained regularized equation, and the detailed error analyses are developed. Finally, some numerical examples are presented to confirm the theory.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2024080

Authors: Daxin Nie, Jing Sun, Weihua Deng

Institution: Lanzhou University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: