Open AccessA GALERKIN FINITE ELEMENT METHOD TO SOLVE FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS
Author(s) -
Alaattin Esen,
Yusuf Uçar,
Nuri Murat Yağmurlu,
Orkun Taşbozan
Publication year - 2013
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2013.783884
Subject(s) - mathematics , fractional calculus , quadratic equation , mathematical analysis , galerkin method , stability (learning theory) , anomalous diffusion , finite element method , diffusion equation , diffusion , wave equation , physics , geometry , innovation diffusion , economy , machine learning , computer science , economics , thermodynamics , service (business) , knowledge management
In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L 2 and L ∞ are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.