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An effective QLM-based Legendre matrix algorithm to solve the coupled system of fractional-order Lane-Emden equations

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dc.contributor.author Izadi, Mohammad
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2024-05-27T11:55:24Z
dc.date.available 2024-05-27T11:55:24Z
dc.date.issued 2024-07
dc.identifier.citation Izadi, Mohammad; Baleanu, Dumitru (2024). "An effective QLM-based Legendre matrix algorithm to solve the coupled system of fractional-order Lane-Emden equations", Applied Numerical Mathematics, Vol. 201, pp. 608-327. tr_TR
dc.identifier.issn 0168-9274
dc.identifier.uri http://hdl.handle.net/20.500.12416/8411
dc.description.abstract The purpose of this study is to propose a computationally effective algorithm for the numerical evaluation of a fractional-order system of singular Lane-Emden type equations arising in physical problems. The fractional operator considered is in the sense of the Liouville-Caputo derivative. The presented matrix collocation method is based upon a combination of the quasilinearization method (QLM) and the shifted Legendre functions (SLFs) and is called QLM-SLFs method. By applying first the QLM to the nonlinear underlying system, we get a family of linear equations. Hence, a spectral matrix collocation scheme relied on the SLFs is designed to solve the resulting sequence of linear system of equations at very few iterations. The uniform convergence of the shifted Legendre expansion series solution is established. To illustrate the effectiveness of the proposed QLM-SLFs technique in the present paper, three test examples are carried out. The applicability and validity of the proposed method are testified through comparisons with the outcomes of other existing procedures in the literature. The proposed QLM-SLFs method is efficient and easy to implement. The approximation obtained by the method also converges quickly to the solutions of the underlying model problem. In comparison with available existing computational procedures, the QLM-SLFs approach shows that the use of Legendre functions together with QLM provides solutions with high accuracy and exponential convergence rate. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1016/j.apnum.2023.12.004 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Collocation Points tr_TR
dc.subject Convergent Analysis tr_TR
dc.subject Coupled Odes tr_TR
dc.subject Lane-Emden Equations tr_TR
dc.subject Liouville-Caputo Fractional Derivative tr_TR
dc.subject Quasilinearization Approach tr_TR
dc.subject Shifted Legendre Functions tr_TR
dc.title An effective QLM-based Legendre matrix algorithm to solve the coupled system of fractional-order Lane-Emden equations tr_TR
dc.type article tr_TR
dc.relation.journal Applied Numerical Mathematics tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 201 tr_TR
dc.identifier.startpage 608 tr_TR
dc.identifier.endpage 627 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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