A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel. Issue 2 (6th November 2019)

• Record Type: Journal Article
• Authors: Xu, Da; Qiu, Wenlin; Guo, Jing
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 2(2020)
• Page Start: 439
• Page End: 458
• Publication Date: 2019-11-06
• Subjects: Cholesky decomposition -- compact difference scheme -- fourth‐order time‐fractional integro‐differential equation -- second‐order convolution quadrature rule -- stability and convergence; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22436
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this paper, a compact finite difference scheme is constructed and investigated for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel. In the temporal direction, the Caputo derivative term is treated by means of L 1 discrete formula and the Riemann–Liouville fractional integral term is discretized by the second‐order convolution quadrature rule. A fully discrete compact difference scheme is constructed with the space discretization by the fourth‐order compact approximation. The stability and convergence are obtained by the discrete energy method, the Cholesky decomposition and the reduced‐order method. Numerical experiments are presented to verify the theoretical analysis.