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Tbilisi Mathematical Journal

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A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations

A. Esen
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  • Inonu University, Faculty of Art and Sciences, Department of Mathematics, 44280 Malatya, Turkey
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/ O. Tasbozan
  • Inonu University, Faculty of Art and Sciences, Department of Mathematics, 44280 Malatya, Turkey
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/ Y. Ucar
  • Inonu University, Faculty of Art and Sciences, Department of Mathematics, 44280 Malatya, Turkey
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/ N.M. Yagmurlu
  • Inonu University, Faculty of Art and Sciences, Department of Mathematics, 44280 Malatya, Turkey
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Published Online: 2015-08-04 | DOI: https://doi.org/10.1515/tmj-2015-0020

Abstract

In this paper, we have considered the fractional diffusion and fractional diffusion- wave equations in which the time derivative is a fractional derivative in the Caputo form and have obtained their numerical solutions by collocation method using cubic B-spline base functions. In the solution process, for the fractional diffusion equation L1 discretizaton formula of the fractional derivative is applied, and for the fractional diffusion-wave equation L2 discretizaton formula of the fractional derivative is applied. Accuracy of the proposed method is discussed by computing the error norms L2 and L . A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.

Keywords: Finite element method; Collocation method; Fractional diffusion equation; Fractional diffusion-wave equation; Cubic B-spline

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About the article

Received: 2015-06-29

Accepted: 2015-07-13

Published Online: 2015-08-04


Citation Information: Tbilisi Mathematical Journal, Volume 8, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2015-0020.

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