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December 2015 A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations
A. Esen, O. Tasbozan, Y. Ucar, N.M. Yagmurlu
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Tbilisi Math. J. 8(2): 181-193 (December 2015). DOI: 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 $L_{2}$ and $L_{\infty}$ . A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.

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A. Esen. O. Tasbozan. Y. Ucar. N.M. Yagmurlu. "A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations." Tbilisi Math. J. 8 (2) 181 - 193, December 2015. https://doi.org/10.1515/tmj-2015-0020

Information

Received: 29 June 2015; Accepted: 13 July 2015; Published: December 2015
First available in Project Euclid: 12 June 2018

zbMATH: 1342.80013
MathSciNet: MR3383792
Digital Object Identifier: 10.1515/tmj-2015-0020

Subjects:
Primary: 80M10
Secondary: 35R11, 45A15, 65L60

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 2 • December 2015
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