High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problem. (5th February 2020)

• Record Type: Journal Article
• Authors: Qiao, Leijie; Xu, Da; Yan, Yubin
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 8(2020)
• Page Start: 5162
• Page End: 5178
• Publication Date: 2020-02-05
• Subjects: convergence -- Crank‐Nicolson alternating direction implicit scheme -- orthogonal spline collocation method -- stability -- two‐dimensional fractional integro‐differential equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6258
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We use the generalized L1 approximation for the Caputo fractional derivative, the second‐order fractional quadrature rule approximation for the integral term, and a classical Crank‐Nicolson alternating direction implicit (ADI) scheme for the time discretization of a new two‐dimensional (2D) fractional integro‐differential equation, in combination with a space discretization by an arbitrary‐order orthogonal spline collocation (OSC) method. The stability of a Crank‐Nicolson ADI OSC scheme is rigourously established, and error estimate is also derived. Finally, some numerical tests are given.