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High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problem
Author(s) -
Qiao Leijie,
Xu Da,
Yan Yubin
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6258
Subject(s) - mathematics , discretization , quadrature (astronomy) , crank–nicolson method , collocation (remote sensing) , spline (mechanical) , alternating direction implicit method , fractional calculus , orthogonal collocation , mathematical analysis , integro differential equation , gaussian quadrature , collocation method , differential equation , nyström method , finite difference method , integral equation , ordinary differential equation , riccati equation , remote sensing , electrical engineering , structural engineering , engineering , geology
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.