A Legendre spectral collocation method for the biharmonic Dirichlet problem
Bernard Bialecki, Andreas Karageorghis (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Bernard Bialecki, Andreas Karageorghis (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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G. Sacchi Landriani, H. Vandeven (1990/91)
Numerische Mathematik
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Bernard Bialecki, Andreas Karageorghis (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is...
Zbigniew Leyk (1986)
Numerische Mathematik
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Mehrnoosh Hedayati, Hojjat Ahsani Tehrani, Alireza Fakharzadeh Jahromi, Mohammad Hadi Noori Skandari, Dumitru Baleanu (2022)
Kybernetika
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One of the most challenging problems in the optimal control theory consists of solving the nonsmooth optimal control problems where several discontinuities may be present in the control variable and derivative of the state variable. Recently some extended spectral collocation methods have been introduced for solving such problems, and a matrix of differentiation is usually used to discretize and to approximate the derivative of the state variable in the particular collocation points....
S. Joe, Y. Yan (1993)
Numerische Mathematik
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Rawashdeh, Edris, McDowell, Dave, Rakesh, Leela (2005)
International Journal of Mathematics and Mathematical Sciences
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S.P. Norsett, H. Brunner (1980/81)
Numerische Mathematik
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