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...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.展开更多
基金supported by University of Macao(File nos.MYRG2020-00035-FST,MYRG2022-00076-FST,MYRG2022-00262-FST).
文摘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.
