 A corrected Crank–Nicolson scheme for the time fractional parabolic integro-differential equation with nonsmooth dataAo Chen, Xuejuan Chen, Yubin Yan and Wen Guo Mathematics and Computers in Simulation (MATCOM), 2026, vol. 242, issue C, 279-296 Abstract: This paper proposes a corrected Crank–Nicolson (CN) scheme for solving time fractional parabolic integro-differential equations which involve Caputo time fractional derivative and fractional Riemann–Liouville (R-L) integral. The weighted and shifted Grünwald–Letnikov (WSGL) formulae is adopted to approximate the time fractional Riemann–Liouville integral. The Crank–Nicolson scheme is applied to approximate the Caputo time fractional derivative. After appropriating corrections, the proposed scheme attains the optimal convergence order of O(τ2) with respect to the time step size τ for both smooth and nonsmooth data at any fixed time t. When combined with the Galerkin finite element method for spatial discretization, it forms a fully discrete scheme. The second-order error estimate for this scheme is rigorously established using the Laplace transform technique and verified by some numerical examples. Keywords: Crank–nicolson scheme; Weighted and shifted Grünwald–Letnikov formulae; Laplace transform; Nonsmooth data (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:242:y:2026:i:c:p:279-296 DOI: 10.1016/j.matcom.2025.12.001 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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