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Least‐squares spectral collocation method for the Stokes equations
Numerical Methods for Partial Differential Equations, 2003AbstractFirst‐order system least‐squares spectral collocation methods are presented for the Stokes equations by adopting the first‐order system and modifying the least‐squares functionals in 2. Then homogeneous Legendre and Chebyshev (continuous and discrete) functionals are shown to be elliptic and continuous with respect to appropriate product ...
Kim, Sang Dong +2 more
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Spectral collocation method for nonlinear Riemann–Liouville fractional differential system
Calcolo, 2021The paper considers the numerical approximations for the Riemann-Liouville fractional differential equations. The model is an IVP of a system of fractional ODEs. The authors consider the integral form of the model, and then apply the spectral collocation method for approximations.
Gu, Zhendong, Kong, Yinying
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Superconvergence of a Chebyshev Spectral Collocation Method
Journal of Scientific Computing, 2007A Chebyshev spectral collocation method is derived for approximating the solution of the second-order two point differential boundary value problems in terms of Chebyshev polynomials \[ u_p= \sum^p_1 a_m\psi_m(x),\quad\psi_m(x)= \int^x_{-1} T_{m-1}(t)\,dt,\;m\geq 1. \] Superconvergence of the derivatives \(u_p'\) at zero's of \(T_m(x)\) is proved.
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Spectral analysis and spectral symbol of matrices in isogeometric collocation methods
Mathematics of Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Donatelli M. +4 more
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A spectral collocation method for compressible, non‐similar boundary layers
International Journal for Numerical Methods in Fluids, 1991AbstractAn efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two‐dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth‐order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation ...
Pruett, C. David, Streett, Craig L.
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A spectral collocation method for mixed functional differential equations
Applied Numerical Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rauch, Reuben +2 more
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Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis, 1996A preconditioning technique for the solution of Chebyshev spectral collocation equations with Dirichlet boundary conditions is analyzed. Bounds for the eigenvalues of the Helmholtz equation are derived. A bilinear finite element preconditioner is proposed where the stiffness matrix is associated with the Chebyshev weight. Hence the preconditioner works
Kim, Sang Dong, Parter, Seymour V.
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A Nonoverlapping Domain Decomposition Method for Legendre Spectral Collocation Problems
Journal of Scientific Computing, 2007This paper deals with the Legendre spectral collocation method in a non-overlapping domain decomposition version to solve Poisson's equation in an \(L\)-shaped region. The collocation equations use Gauss-Legendre nodes instead of the more usual Gauss-Legendre-Lobatto points. The problem is decoupled into several independent steps.
Bialecki, B. +3 more
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Spectral Collocation Methods for Differential-Algebraic Equations with Arbitrary Index
Journal of Scientific Computing, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Can, Zhang, Zhimin
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The chain collocation method: A spectrally accurate calculus of forms
Journal of Computational Physics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rufat, Dzhelil +3 more
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