Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations

The principal aim of the current paper is to present and analyze two new spectral algorithms for solving some types of linear and nonlinear fractional-order differential equations. The proposed algorithms are obtained by utilizing a certain kind of shifted Chebyshev polynomials called the shifted fi...

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Veröffentlicht in:Computational & applied mathematics Jg. 37; H. 3; S. 2897 - 2921
Hauptverfasser: Abd-Elhameed, W. M., Youssri, Y. H.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.07.2018
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Applied physics
Basis functions
Chebyshev approximation
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Error analysis
Ice
Liouville theorem
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Nonlinear equations
Polynomials
33C45
Fractional differential equations
11B83
65M70
Fifth-kind Chebyshev polynomials
Connection problem
Spectral methods
Romberg’s quadrature formulae
34A08
ISSN:0101-8205, 2238-3603, 1807-0302
Online-Zugang:Volltext
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Zusammenfassung:The principal aim of the current paper is to present and analyze two new spectral algorithms for solving some types of linear and nonlinear fractional-order differential equations. The proposed algorithms are obtained by utilizing a certain kind of shifted Chebyshev polynomials called the shifted fifth-kind Chebyshev polynomials as basis functions along with the application of a modified spectral tau method. The class of fifth-kind Chebyshev polynomials is a special class of a basic class of symmetric orthogonal polynomials which are constructed with the aid of the extended Sturm–Liouville theorem for symmetric functions. An investigation for the convergence and error analysis of the proposed Chebyshev expansion is performed. For this purpose, a new connection formulae between Chebyshev polynomials of the first and fifth kinds are derived. The obtained numerical results ascertain that our two proposed algorithms are applicable, efficient and accurate.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-017-0488-z