Open Access

ARTICLE

Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation

Muhammad Amin¹, Muhammad Abbas^2,*, Dumitru Baleanu^3,4,5, Muhammad Kashif Iqbal⁶, Muhammad Bilal Riaz⁷

1 Department of Mathematics, National College of Business Administration & Economics, Lahore, 54660, Pakistan
2 Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan
3 Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
5 Institute of Space-Sciences, Bucharest, 077125, Romania
6 Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan
7 Department of Mathematics, University of Management and Technology, Lahore, 54700, Pakistan

* Corresponding Author: Muhammad Abbas. Email:

(This article belongs to the Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 127(1), 361-384. https://doi.org/10.32604/cmes.2021.012720

Received 10 July 2020; Accepted 21 December 2020; Issue published 30 March 2021

Abstract

This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.

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