A Compact Difference Scheme on Graded Meshes for the Nonlinear Fractional Integro-differential Equation with Non-smooth Solutions  

作　　者：Da-kang CEN Zhi-bo WANG Yan MO 

机构地区：[1]School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510006,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第3期601-613,共13页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11701103,11801095);Young Top-notch Talent Program of Guangdong Province(No.2017GC010379);Natural Science Foundation of Guangdong Province(No.2022A1515012147,2019A1515010876,2017A030310538);the Project of Science and Technology of Guangzhou(No.201904010341,202102020704);the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(2021023)。

摘　　要：In this paper,a compact finite difference scheme for the nonlinear fractional integro-differential equation with weak singularity at the initial time is developed,with O(N^(-(2-α))+M^(-4))accuracy order,where N;M denote the numbers of grids in temporal and spatial direction,α ∈(0,1)is the fractional order.To recover the full accuracy based on the regularity requirement of the solution,we adopt the L1 method and the trapezoidal product integration(PI)rule with graded meshes to discretize the Caputo derivative and the Riemann-Liouville integral,respectively,further handle the nonlinear term carefully by the Newton linearized method.Based on the discrete fractional Gr¨onwall inequality and preserved discrete coefficients of Riemann-Liouville fractional integral,the stability and convergence of the proposed scheme are analyzed by the energy method.Theoretical results are also confirmed by a numerical example.

关 键 词：nonlinear fractional integro-differential equation graded meshes discrete fractional Gr?nwall inequality compact difference scheme stability and convergence 

分 类 号：O175[理学—数学]