<abstract xmlns="http://www.w3.org/1999/xhtml">This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order <italic>O</italic>(<italic>τ</italic>2−α+ <italic>h</italic>4) in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.</abstract>

This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4) in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

A numerical solution for a class of time fractional diffusion equations with delay

Department of Computational Mathematics and Computer Science

Department of Mathematics, Faculty of Science

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence...

A numerical solution for a class of time fractional diffusion equations with delay

Published Online: Sep 23, 2017

Page range: 477 - 488

Received: Nov 29, 2016

Accepted: May 04, 2017

DOI: https://doi.org/10.1515/amcs-2017-0033

Keywords
fractional diffusion equation with delay, difference scheme, convergence analysis

© 2017 Vladimir G. Pimenov et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A numerical solution for a class of time fractional diffusion equations with delay

Published Online: Sep 23, 2017

Page range: 477 - 488

Received: Nov 29, 2016

Accepted: May 04, 2017

DOI: https://doi.org/10.1515/amcs-2017-0033

Keywordsfractional diffusion equation with delay, difference scheme, convergence analysis

© 2017 Vladimir G. Pimenov et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fractional diffusion equation with delay, difference scheme, convergence analysis