Extended Cubic B-Splines in the Numerical Solution of Time Fractional Telegraph Equation
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Date
2019
Journal Title
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Volume Title
Publisher
Springer
Open Access Color
GOLD
Green Open Access
No
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Top 10%
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Abstract
A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.
Description
Akram, Tayyaba/0000-0002-1825-2631; Abbas, Dr. Muhammad/0000-0002-0491-1528
Keywords
Time Fractional Telegraph Equation, Extended Cubic B-Spline Basis Functions, Collocation Method, Caputo'S Fractional Derivative, Stability Analysis, Convergence, Caputo’s fractional derivative, Telegrapher's equations, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, Differential equation, Time fractional telegraph equation, Numerical Methods for Singularly Perturbed Problems, Transmission line, QA1-939, FOS: Mathematics, Collocation method, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Extended cubic B-spline basis functions, Time-Fractional Diffusion Equation, Stability analysis, Partial differential equation, Applied mathematics, Computer science, Fractional Derivatives, Modeling and Simulation, Physical Sciences, Telecommunications, Fractional Calculus, Convergence, Finite Difference Schemes, Mathematics, Ordinary differential equation, time fractional telegraph equation, stability analysis, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Caputo's fractional derivative, extended cubic B-spline basis functions, convergence, Fractional partial differential equations, collocation method, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Akram, Tayyaba...et al. (2019). "Extended cubic B-splines in the numerical solution of time fractional telegraph equation", Advances in Difference Equations, Vol. 2019, No. 1.
WoS Q
Q1
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OpenCitations Citation Count
34
Source
Advances in Difference Equations
Volume
2019
Issue
1
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CrossRef : 28
Scopus : 35
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