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

• Autorzy: Béla J. Szekeres , Ferenc Izsák
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fractional order diffusion; Grünwald–Letnikov formula; Non-local derivative; Neumann boundaryconditions; Implicit Euler scheme

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-03-05

zaakceptowano

2015-05-15

online

2015-09-25

Twórcy

autor

Béla J. Szekeres

• Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, H-1117, Budapest,
  Pázmány P. s. 1/C, Hungary

autor

Ferenc Izsák

• Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, H-1117, Budapest,
  Pázmány P. s. 1/C, Hungary
• MTA-ELTE NumNet Research Group, Eötvös Loránd University, 1117 Budapest,
  Pázmány P. stny. 1C, Hungary

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Identyfikatory

DOI

10.1515/math-2015-0056