Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem

作     者：Jing Sun Weihua Deng Daxin Nie 

作者机构：School of Mathematics and StatisticsGansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000P.R.China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2022年第15卷第3期

页      面：744-767页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant No.12071195) the AI and Big Data Funds(Grant No.2019620005000775) by the Fundamental Research Funds for the Central Universities(Grant Nos.lzujbky-2021-it26,lzujbky-2021-kb15) NSF of Gansu(Grant No.21JR7RA537). 

主　　题：One-and two-dimensional integral fractional Laplacian Lagrange interpolation operator splitting finite difference the inhomogeneous fractional Dirichlet problem error estimates 

摘      要：We make the split of the integral fractional Laplacian as(−△
)^(s)u=(−△
)(−△
)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplacian with the inhomogeneous Dirichlet boundary condition and give the corresponding truncation errors with the help of the interpolation estimate.Moreover,the suitable corrections are proposed to guarantee the convergence in solving the inhomogeneous fractional Dirichlet problem and an O(h^(1+α)2s))convergence rate is obtained when the solution u∈C^(1,α)(Ω_(n)^(δ)),where n is the dimension of the space,∈(max(0,2s−1),1],δis a fixed positive constant,and h denotes mesh size.Finally,the performed numerical experiments confirm the theoretical results.