Open AccessMittag-Leffler-Pade approximations for the numerical solution of space and time fractional diffusion equations
Author(s) -
A. Borhanifar,
Sohrab Valizadeh
Publication year - 2015
Publication title -
international journal of applied mathematical research
Language(s) - English
Resource type - Journals
ISSN - 2227-4324
DOI - 10.14419/ijamr.v4i4.4340
Subject(s) - mathematics , padé approximant , truncation error , fractional calculus , relaxation (psychology) , exponential function , mittag leffler function , mathematical analysis , diffusion , numerical analysis , space (punctuation) , anomalous diffusion , diffusion equation , innovation diffusion , physics , psychology , social psychology , linguistics , philosophy , knowledge management , economy , computer science , economics , service (business) , thermodynamics
Anomalous diffusion and non-exponential relaxation patterns can be described by a space - time fractional diffusion equation. This paper aims to present a Pade approximation for Mittag-Leffler function mixed finite difference method to develop a numerical method to obtain an approximate solution for the space and time fractional diffusion equation. The truncation error of the method is theoretically analyzed. It is proved that the numerical proposed method is unconditionally stable from the matrix analysis point of view. Finally, some numerical results are given, which demonstrate the efficiency of the approximate scheme.