An ADI orthogonal spline collocation method for a new two-dimensional distributed-order fractional integro-differential equation. (15th February 2023)

• Record Type: Journal Article
• Authors: Tang, Bo; Qiao, Leijie; Xu, Da
• Is Part Of: Computers & mathematics with applications. Volume 132(2023)
• Page Start: 104
• Page End: 118
• Publication Date: 2023-02-15
• Subjects: Distributed-order time-fractional derivative -- Riemann-Liouville fractional integral -- Alternating direction implicit method -- Orthogonal spline collocation method -- Stability and convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.12.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider an alternating direction implicit (ADI) scheme combined with an arbitrary-order orthogonal spline collocation (OSC) method in space for the numerical solution of the distributed-order fractional integro-differential equation. The weighted and shifted Grünwald formula is employed to discretize the distributed-order time-fractional derivative combined with the second-order fractional quadrature convolution rule introduced by Lubich for the Riemann-Liouville fractional integral. We prove the stability of the proposed ADI OSC scheme and derive error estimates. Finally, some numerical tests are given.