AUTHOR=Amin Muhammad , Abbas Muhammad , Iqbal Muhammad Kashif , Baleanu Dumitru 

TITLE=Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00288

DOI=10.3389/fphy.2020.00288

ISSN=2296-424X

ABSTRACT=In this work, we have developed a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution for time fractional Klein--Gorden equation. The presented technique engages finite difference formulation for discretizing the Caputo time fractional derivative of order $\alpha \in (1,2]$ and redefined extended cubic B-spline functions to interpolate the solution curve along spatial grid. A stability analysis of the scheme is set up to affirm that the errors do not amplify during the execution of numerical procedure. The derivation of uniform convergence reveals that the scheme is $O(h^{2}+\Delta t^{2-\alpha})$ accurate. Some computational experiments are carried out to verify the theoretical considerations. Numerical results are compared with the existing techniques on the topic and it is concluded that the present scheme returns superior outcomes.