A backward euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation

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

来源：Numerical Methods for Partial Differential Equations, 2015, 31(5): 1534-1550.

DOI：10.1002/num.21958

• time-fractional Fokker-Planck equation
• orthogonal spline collocation method
• Caputo derivative
• backward Euler method
• stability
• convergence
• superconvergence

We formulate and analyze a novel numerical method for solving a time-fractional Fokker-Planck equation which models an anomalous subdiffusion process. In this method, orthogonal spline collocation is used for the spatial discretization and the time-stepping is done using a backward Euler method based on the L1 approximation to the Caputo derivative. The stability and convergence of the method are considered, and the theoretical results are supported by numerical examples, which also exhibit superconvergence.

• 出版日期2015-9
• 单位湖南师范大学; 湖南工业大学