Numerical solution of systems of fractional delay differential equations using a new kind of wavelet basis

In the present paper, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet basis and their properties are utilized to obtain their operational matrix of fractional integration in the Riemann–Liouville sense and delay operat...

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Vydané v:	Computational & applied mathematics Ročník 37; číslo 4; s. 4122 - 4144
Hlavný autor:	Mohammadi, Fakhrodin
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cham Springer International Publishing 01.09.2018 Springer Nature B.V
Predmet:	Applications of Mathematics Applied physics Computational mathematics Computational Mathematics and Numerical Analysis Delay Differential equations Error detection Galerkin method Mathematical analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Wavelet analysis Wavelet transforms Chelyshkov wavelet Caputo derivative Chelyshkov polynomials Operational matrix Galerkin method Systems of fractional delay differential equations 65T60 Convergence analysis 37L65 34A08
ISSN:	0101-8205, 2238-3603, 1807-0302
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Popis
Shrnutí:	In the present paper, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet basis and their properties are utilized to obtain their operational matrix of fractional integration in the Riemann–Liouville sense and delay operational matrix. Convergence and error bound of the expansion by this kind of wavelet functions are investigated. Then, these operational matrices along with the Galerkin approach have been implemented to solve systems of fractional delay differential equations (SFDDEs). The main superiority of the proposed technique is that it reduces SFDDEs to a system of algebraic equations. Moreover, accuracy and efficiency of the suggested Chelyshkov wavelet approach are verified through some linear and nonlinear SFDDEs. Finally, the obtained numerical results are compared with those previously reported in the literature.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0101-8205 2238-3603 1807-0302
DOI:	10.1007/s40314-017-0550-x