3 papers
math.NA2023
Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution
Daxin Nie, Jing Sun, Weihua Deng
Finite difference method as a popular numerical method has been widely used to solve fractional diffusion equations. In the general spatial error analyses, an assumption $u\in C^{4…
math.NA2022
Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise
Jing Sun, Daxin Nie, Weihua Deng
Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competitio…
math.NA2021
Regularity theory and numerical algorithm for the fractional Klein-Kramers equation
Jing Sun, Daxin Nie, Weihua Deng
Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for fractional Klein-Kramers equation based on…