Generalized Laguerre pseudospectral method based Laguerre interpolation

Xiao-yong, Zhang; Yan, Li

doi:10.1016/j.amc.2012.08.090

Cited by 6 publications

(1 citation statement)

References 40 publications

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“…The authors of [ 33 ] proposed a new orthogonal family of generalized Laguerre functions to approximate the solution of differential equations of degenerate type. Xiao-Yong and Yan [ 34 ] investigated a pseudospectral scheme based on a class of modified generalized Laguerre to introduce a very efficient method for solving second-order differential equation in a long-time interval. Gulsu et al [ 35 ] presented the Laguerre collocation method for solving a class of delay difference equations.…”

Section: Introductionmentioning

confidence: 99%

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

Bhrawy

Taha

Alzahrani

et al. 2015

PLoS ONEHas correction 2015-9-14 Has erratum 2015-9-14 Has erratum 2015-10-30

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In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

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Section: Introductionmentioning

confidence: 99%