Boundary value problems for the diffusion equation of the variable order in differential and difference settings
Numerical Analysis
2012-11-22 v2 Mathematical Physics
math.MP
Abstract
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori estimates for these problems exactly as in the classical case. The credibility of the obtained results is verified by performing numerical calculations for a test problem.
Cite
@article{arxiv.1105.2033,
title = {Boundary value problems for the diffusion equation of the variable order in differential and difference settings},
author = {A. A. Alikhanov},
journal= {arXiv preprint arXiv:1105.2033},
year = {2012}
}
Comments
19 pages. Presented at the 4-th IFAC Workshop on Fractional Differentiation and Its Applications, Badajoz, Spain, October 18-20, 2010