On a numerical investigation of the time fractional Fokker– Planck equation via local discontinuous Galerkin method. Issue 9 (2nd September 2017)

• Record Type: Journal Article
• Authors: Eshaghi, Jafar; Adibi, Hojatollah; Kazem, Saeed
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 9(2017)
• Page Start: 1916
• Page End: 1942
• Publication Date: 2017-09-02
• Subjects: Time fractional Fokker–Planck equation -- discontinuous Galerkin method -- local discontinuous Galerkin method -- Caputo derivative -- Mittag–Leffler function -- stability and convergence analysis; 45D05 -- 45G05 -- 41A30; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2016.1247442
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: This paper presents two numerical solutions of time fractional Fokker– Planck equations (TFFPE) based on the local discontinuous Galerkin method (LDGM). Two time-discretization schemes for the fractional order part of TFFPE are investigated. The first discretization utilizes the fractional finite difference scheme (FFDS) and in the second scheme the fractional derivative is replaced by the Volterra integral equation which it computed by the trapezoidal quadrature scheme (TQS). Then the LDGM has been applied for space-discretization in both schemes. Additionally, the stability and convergence analysis of the proposed methods have been discussed. Finally some test problems have been investigated to confirm the validity and convergence of two proposed methods. The results show that FFDS and TQS are2 − α and second-order accurate in time variable, respectively.