Research On Finite Difference Schemes Of Fractional Laplace Equation

In this paper,we mainly study the numerical quadrature formulas of fractional Laplacian operators and the limitations of fractional Laplacian equations.Firstly,based on the definition of singular integral of fractional Laplace operator,two new numerical quadrature formulas are proposed.The optimal error analysis is given.Then,based on these two quadrature formulas,two finite difference schemes for Dirichlet boundary value problem of fractional Laplace equation are constructed.The corresponding convergence order analysis is given.Finally,some numerical examples are given,and the results show the validity of the algorithm and the correctness of the theoretical analysis.