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- Title
A Compact Difference Scheme on Graded Meshes for the Fourth-order Fractional Integro-differential Equation with Initial Singularity.
- Authors
Yaoyao Zhang; Dakang Cen; Zhibo Wang
- Abstract
In this paper, a compact finite difference scheme is constructed and investigated for the fourth-order time-fractional integro-differential equation with singular kernels. In temporal direction, the Caputo derivative is treated by L1 discrete formula and the Riemann-Liouville fractional integral is discretized by trapezoidal PI rule respectively. In spatial direction, the fourth order derivative is approximating by high-order accuracy compact difference method. The detailed analysis shows that the proposed scheme is unconditionally stable and convergent with the convergence order O(N-min{rσ,2-α} + M-4). N,M denote the numbers of grids in temporal direction and in spatial direction, α ∊ (0, 1) is the fractional order of the Caputo derivative and -4 is a regularity parameter. At last, some numerical results are also given to confirm our theoretical statement.
- Subjects
FINITE differences; INTEGRO-differential equations; CAPUTO fractional derivatives; FRACTIONAL integrals; IMAGE encryption; MESH networks
- Publication
Southeast Asian Bulletin of Mathematics, 2023, Vol 47, Issue 5, p721
- ISSN
0129-2021
- Publication type
Article