Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation

The operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shifted Chebyshev polynomials, are presented and derived. We propose an accurate and efficient spectral algorithm for the numerical solution of the two-si...

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Vydané v:	Journal of optimization theory and applications Ročník 174; číslo 1; s. 321 - 341
Hlavní autori:	Bhrawy, Ali H., Zaky, Mahmoud A., Machado, José A. Tenreiro
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.07.2017 Springer Nature B.V
Predmet:	Accuracy Algebra Algorithms Applications of Mathematics Boundary conditions Calculus of Variations and Optimal Control; Optimization Chebyshev approximation Dirichlet problem Engineering Iterative methods Mathematics Mathematics and Statistics Matrices (mathematics) Operations Research/Decision Theory Optimization Polynomials Simplification Spacetime Theory of Computation Operational matrix Fractional telegraph equation Riesz fractional derivative Fractional Klein–Gordon equation Shifted Chebyshev Tau method
ISSN:	0022-3239, 1573-2878
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Abstract	The operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shifted Chebyshev polynomials, are presented and derived. We propose an accurate and efficient spectral algorithm for the numerical solution of the two-sided space–time Caputo fractional-order telegraph equation with three types of non-homogeneous boundary conditions, namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based on shifted Chebyshev tau technique combined with the derived shifted Chebyshev operational matrices. We focus primarily on implementing the novel algorithm both in temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations greatly simplifying the problem. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.
AbstractList	The operational matrices of left Caputo fractional derivative, right Caputo fractional derivative, and Riemann–Liouville fractional integral, for shifted Chebyshev polynomials, are presented and derived. We propose an accurate and efficient spectral algorithm for the numerical solution of the two-sided space–time Caputo fractional-order telegraph equation with three types of non-homogeneous boundary conditions, namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based on shifted Chebyshev tau technique combined with the derived shifted Chebyshev operational matrices. We focus primarily on implementing the novel algorithm both in temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations greatly simplifying the problem. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.
Author	Machado, José A. Tenreiro Bhrawy, Ali H. Zaky, Mahmoud A.
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SubjectTerms	Accuracy Algebra Algorithms Applications of Mathematics Boundary conditions Calculus of Variations and Optimal Control; Optimization Chebyshev approximation Dirichlet problem Engineering Iterative methods Mathematics Mathematics and Statistics Matrices (mathematics) Operations Research/Decision Theory Optimization Polynomials Simplification Spacetime Theory of Computation
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Title	Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation
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