High-order ADI orthogonal spline collocation method for a new 2D fractional integro-differential problem |
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| Authors: | Leijie Qiao Da Xu Yubin Yan |
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| Affiliation: | 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, China;2. Department of Mathematics, Hunan Normal University, Changsha, Hunan, China;3. Department of Mathematical and Physical Science, University of Chester, Thornton Science Park, Chester, UK |
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| 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. |
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| Keywords: | convergence Crank-Nicolson alternating direction implicit scheme orthogonal spline collocation method stability two-dimensional fractional integro-differential equation |
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