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2015 | 13 | 1 |
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-03-05
zaakceptowano
2015-05-15
online
2015-09-25
Twórcy
  • Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, H-1117, Budapest,
    Pázmány P. s. 1/C, Hungary
  • 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
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0056
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