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 Li 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?nwall 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.

Da-kang CEN;Zhi-bo WANG;Yan MO

School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510006,China

应用数学学报（英文版）

[1]Da-kang CEN;Zhi-bo WANG;Yan MO-.A Compact Difference Scheme on Graded Meshes for the Nonlinear Fractional Integro-differential Equation with Non-smooth Solutions)[J].应用数学学报（英文版）,2022(03):601-613

Meshes,Integro,nwall

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