ALTERNATING DIRECTION IMPLICIT OSC SCHEME FOR THE TWO-DIMENSIONAL FRACTIONAL EVOLUTION EQUATION WITH A WEAKLY SINGULAR KERNEL

作者：Zhang, Haixiang; Yang, Xuehua^*; Xu, Da

来源：Acta Mathematica Scientia, 2018, 38(6): 1689-1711.

DOI：10.1016/S0252-9602(18)30840-3

• fractional equation
• orthogonal spline collocation scheme
• alternating direction implicit
• stability
• convergence

In this paper, a new kind of alternating direction implicit (ADI) Crank-Nicolsontype orthogonal spline collocation (OSC) method is formulated for the two-dimensional fractional evolution equation with a weakly singular kernel arising in the theory of linear viscoelasticity. The novel OSC method is used for the spatial discretization, and ADI Crank-Nicolsontype method combined with the second order fractional quadrature rule are considered for the temporal component. The stability of proposed scheme is rigourously established, and nearly optimal order error estimate is also derived. Numerical experiments are conducted to support the predicted convergence rates and also exhibit expected super-convergence phenomena.

• 出版日期2018-11
• 单位北京应用物理与计算数学研究所; 湖南工业大学; 湖南师范大学