Numerical solution of fractional order advection-reaction diffusion equation
Document Type
Article
Publication Date
1-1-2018
Abstract
In this paper, the Laplace transform method is used to solve the advection-diffusion equation having source or sink term with initial and boundary conditions. The solution profile of normalized field variable for both conservative and non-conservative systems are calculated numerically using the Bellman method and the results are presented through graphs for different particular cases. A comparison of the numerical solution with the existing analytical solution for standard order conservative system clearly exhibits that the method is effective and reliable. The important part of the study is the graphical presentations of the effect of the reaction term on the solution profile for the non-conservative case in the fractional order as well as standard order system. The salient feature of the article is the exhibition of stochastic nature of the considered fractional order model.
Keywords
advection, diffusion, Laplace transformation, conservative system, non-conservative system, evolutionary process
Divisions
MathematicalSciences
Funders
Science & Engineering Research Board (SERB),Government of India vide their letter number SB/S4/MS:840/13 dated 07.05.2015,Fundamental Research Grant Scheme, Ministry of Higher Education, Malaysia [FP045-2015A]
Publication Title
Thermal Science
Volume
22
Issue
Suppl.
Publisher
VINCA Institute of Nuclear Sciences