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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 25, 2015

A finite difference method for fractional diffusion equations with Neumann boundary conditions

  • Béla J. Szekeres and Ferenc Izsák
From the journal Open Mathematics

Abstract

A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. The basis of the mathematical model and the numerical approximation is an appropriate extension of the initial values, which incorporates homogeneous Dirichlet or Neumann type boundary conditions. The wellposedness of the obtained initial value problem is proved and it is pointed out that each extension is compatible with the original boundary conditions. Accordingly, a finite difference scheme is constructed for the Neumann problem using the shifted Grünwald–Letnikov approximation of the fractional order derivatives, which is based on infinite many basis points. The corresponding matrix is expressed in a closed form and the convergence of an appropriate implicit Euler scheme is proved.

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Received: 2015-3-5
Accepted: 2015-5-15
Published Online: 2015-9-25

©2015 Béla J. Szekeres and Ferenc Izsák

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

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