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Open AccessArticle

Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation

1
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
2
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
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Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudia Arabia
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Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, Turkey
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Institute of Space-Sciences, Magurele-Bucharest 077125, Romania
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Department of Physics, College of Applied Sciences, Palestine Technical University-Kadoorie, Tulkarm 303, Palestine
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1154; https://doi.org/10.3390/sym12071154
Received: 16 June 2020 / Revised: 1 July 2020 / Accepted: 7 July 2020 / Published: 10 July 2020
(This article belongs to the Special Issue Advanced Calculus in Problems with Symmetry)
The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor’s series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method. View Full-Text
Keywords: Nonlinear time fractional telegraph equation; extended cubic B-spline basis; collocation method; Caputo’s fractional derivative Nonlinear time fractional telegraph equation; extended cubic B-spline basis; collocation method; Caputo’s fractional derivative
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MDPI and ACS Style

Akram, T.; Abbas, M.; Iqbal, A.; Baleanu, D.; Asad, J.H. Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation. Symmetry 2020, 12, 1154. https://doi.org/10.3390/sym12071154

AMA Style

Akram T, Abbas M, Iqbal A, Baleanu D, Asad JH. Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation. Symmetry. 2020; 12(7):1154. https://doi.org/10.3390/sym12071154

Chicago/Turabian Style

Akram, Tayyaba; Abbas, Muhammad; Iqbal, Azhar; Baleanu, Dumitru; Asad, Jihad H. 2020. "Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation" Symmetry 12, no. 7: 1154. https://doi.org/10.3390/sym12071154

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