Finite difference and local discontinuous Galerkin methods for fourth-order time-fractional partial integro-differential equation: Computational approach for one-dimensional case

Karamali, Gholamreza; Mohammadi-firouzjaei, Hadi

doi:10.22080/cjms.2024.27625.1713

Finite difference and local discontinuous Galerkin methods for fourth-order time-fractional partial integro-differential equation: Computational approach for one-dimensional case

Document Type : Research Articles

Authors

¹ Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran

² Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South MehrAbad, Tehran, Iran.

10.22080/cjms.2024.27625.1713

Abstract

‎‎Our focus in this paper is on numerically solving fourthorder time-fractional integro-dierential equations with weakly singular kernels. L1 and quadrature formulas are used to discretize the temporal and memory terms. For spatial discretization, a highorder local discontinuous Galerkin method is employed. Finally, the numerical optimal convergence rate for the proposed scheme is demonstrated by the use of numerical results.

Keywords