A backward euler orthogonal spline collocation method for the time‐fractional Fokker–Planck equation. Issue 5 (28th December 2014)

• Record Type: Journal Article
• Authors: Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da
• Is Part Of: Numerical methods for partial differential equations. Volume 31:Issue 5(2015)
• Page Start: 1534
• Page End: 1550
• Publication Date: 2014-12-28
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21958
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1534–1550, 2015</p> </abstract>