Fitted L1-ADI Scheme for Improving Convergence of Two-Dimensional Delay Fractional Equations

doi:10.1007/s42967-023-00363-w

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (6): 2173-2188.doi: 10.1007/s42967-023-00363-w

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Fitted L1-ADI Scheme for Improving Convergence of Two-Dimensional Delay Fractional Equations

Xiaoqing Pan, Xiaotong Huang, Dakang Cen, Siu-Long Lei, Seakweng Vong

Department of Mathematics, University of Macau, Macao, China

Received:2023-08-18 Revised:2023-11-27 Published:2025-12-24
Contact: Dakang Cen, E-mail:cendakang@163.com E-mail:cendakang@163.com
Supported by:
This research is supported by University of Macau (File nos. MYRG2020-00035-FST, MYRG2022-00076-FST, MYRG2022-00262-FST).

Abstract

Abstract: In this paper, the regularity and finite difference methods for the two-dimensional delay fractional equations are considered. The analytic solution is derived by eigenvalue expansions and Laplace transformation. However, due to the derivative discontinuities resulting from the delay effect, the traditional L1-ADI scheme fails to achieve the optimal convergence order. To overcome this issue and improve the convergence order, a simple and cost-effective decomposition technique is introduced and a fitted L1-ADI scheme is proposed. The numerical tests are conducted to verify the theoretical result.

Key words: Two-dimensional delay fractional equations, Derivative discontinuity, Cost-effective decomposition technique, Fitted L1-ADI scheme

CLC Number:

Xiaoqing Pan, Xiaotong Huang, Dakang Cen, Siu-Long Lei, Seakweng Vong. Fitted L1-ADI Scheme for Improving Convergence of Two-Dimensional Delay Fractional Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(6): 2173-2188.

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Fitted L1-ADI Scheme for Improving Convergence of Two-Dimensional Delay Fractional Equations

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