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Legendre polynomials 2

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Generalized Hamilton-Jacobi-Bellman equation 1

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Galerkin approximationwith Legendre polynomials for a continuous-time nonlinear optimal control problem Article

Xue-song CHEN

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 10, Pages 1479-1487 doi: 10.1631/FITEE.1601101

Abstract: The Galerkin approximation with Legendre polynomials (GALP) for GHJB equations has not been applied toThe integrals that need to be computed are much fewer due to the orthogonal properties of Legendre polynomials

Keywords： Generalized Hamilton-Jacobi-Bellman equation Nonlinear optimal control Galerkin approximation Legendre

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Synchronization of two different chaotic systems using Legendre polynomials with applications in secure None

Saeed KHORASHADIZADEH, Mohammad-Hassan MAJIDI

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 9, Pages 1180-1190 doi: 10.1631/FITEE.1601814

Abstract: It consists of a state feedback controller and a robust control term using Legendre polynomials to compensateDue to the orthogonal functions theorem, Legendre polynomials can approximate nonlinear functions withLegendre polynomials have fewer tuning parameters than fuzzy systems and neural networks.Similar to the parameters of fuzzy systems, Legendre coefficients are estimated online using the adaptation

Keywords： Observer-based synchronization Chaotic systems Legendre polynomials Secure communications

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Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU, Kezhen YAN, Jianhong MAN, Nengyuan LIU

Frontiers of Structural and Civil Engineering 2020, Volume 14, Issue 3, Pages 632-645 doi: 10.1007/s11709-020-0617-4

Abstract: Gauss-Legendre quadrature is a key scheme in the numerical inversion process.

Keywords： multi-layered structure Hankel transformation anisotropic transversely isotropic interlayer condition Gauss-Legendre

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High-precision Numerical Computation of High-degree Gauss quadrature Nodes

Zhang Qingli,Wang Xiaomei,Yin Shaotang,Jiang Haihe

Strategic Study of CAE 2008, Volume 10, Issue 2, Pages 35-40

Abstract: A method to compute the zeroes of the high-degree Legendre, Laguerre and Hermite polynomials, which arethe nodes of Gauss-Legendre, Gauss-Laguerre and Gauss-Hermite Quadrature, respectively, is studied,According to the properties of Legendre, Laguerre and Hermite polynomials, their definitions are modifiedNumerical experiments indicate that the method is very efficient and the high-precise roots of Legendre

Keywords： Gauss quadrature Legendre polynomial Laguerre polynomial Hermite polynomial extract roots