<abstract xmlns="http://www.w3.org/1999/xhtml">

In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The <italic>L</italic>1and <italic>L</italic>2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms <italic>L</italic>2 and <italic>L</italic>∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs).
</abstract>

In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The L1and L2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms L2 and L∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs).

Collocation solutions for the time fractional telegraph equation using cubic B-spline finite elements

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional...

Collocation solutions for the time fractional telegraph equation using cubic B-spline finite elements

Published Online: Dec 21, 2020

Page range: 131 - 144

DOI: https://doi.org/10.2478/awutm-2019-0020

Keywords
Finite Element Method, Collocation Method, Time Fractional Telegraph Equation, Cubic B-Spline

© 2019 Orkun Tasbozan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Collocation solutions for the time fractional telegraph equation using cubic B-spline finite elements

Published Online: Dec 21, 2020

Page range: 131 - 144

DOI: https://doi.org/10.2478/awutm-2019-0020

KeywordsFinite Element Method, Collocation Method, Time Fractional Telegraph Equation, Cubic B-Spline

© 2019 Orkun Tasbozan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Finite Element Method, Collocation Method, Time Fractional Telegraph Equation, Cubic B-Spline