In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly s...In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly singular kernel arising in the theory of linear viscoelas-ticity. The novel OSC method is used for the spatial discretization, and ADI Crank-Nicolson-type method combined with the second order fractional quadrature rule are considered for thetemporal component. The stability of proposed scheme is rigourously established, and nearlyoptimal order error estimate is also derived. Numerical experiments are conducted to supportthe predicted convergence rates and also exhibit expected super-convergence phenomena.展开更多
基金supported by National Nature Science Foundation of China(11701168,11601144 and 11626096)Hunan Provincial Natural Science Foundation of China(2018JJ3108,2018JJ3109 and 2018JJ4062)+1 种基金Scientific Research Fund of Hunan Provincial Education Department(16K026 and YB2016B033)China Postdoctoral Science Foundation(2018M631403)
文摘In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly singular kernel arising in the theory of linear viscoelas-ticity. The novel OSC method is used for the spatial discretization, and ADI Crank-Nicolson-type method combined with the second order fractional quadrature rule are considered for thetemporal component. The stability of proposed scheme is rigourously established, and nearlyoptimal order error estimate is also derived. Numerical experiments are conducted to supportthe predicted convergence rates and also exhibit expected super-convergence phenomena.
