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Numerical studies on nonlinear Schrödinger equations by spectral collocation method with preconditioning

Journal of Mathematical Analysis and Applications, 2007
In this study, we use the spectral collocation method with preconditioning to solve various nonlinear Schrödinger equations. To reduce round-off error in spectral collocation method we use preconditioning.
A Golbabai
exaly   +2 more sources

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Spectral collocation in space and time for linear PDEs

Journal of Computational Physics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. H. Lui 0001, Sarah Nataj
openaire   +2 more sources

Fractional Spectral Collocation Method

SIAM Journal on Scientific Computing, 2014
We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points.
Mohsen Zayernouri, George E. Karniadakis
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Spectral collocation methods for polymer brushes

The Journal of Chemical Physics, 2011
We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging in the past because of sharp features that arise in the self-consistent pressure field at ...
Tanya L, Chantawansri, Su-Mi, Hur, Carlos J, García-Cervera, Hector D, Ceniceros, Glenn H, Fredrickson   +4 more
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Improved Resolution of Boundary Layers for Spectral Collocation

SIAM Journal on Scientific Computing, 2019
The authors of this article consider singularly perturbed two-point boundary value problems in one dimension. They derive an algorithm based on the regularized sine-transformation with and without resampling in order to improve the accuracy of the spectral method.
Conor McCoid, Manfred R. Trummer
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Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations

SIAM Journal on Scientific Computing, 2010
This paper is concerned with the spectral Chebyshev collocation solution of the Dirichlet problems for the Poisson and biharmonic equations in a square. The collocation schemes are solved at a cost of $2N^3+O(N^2\log N)$ operations using an appropriate set of basis functions, a matrix diagonalization algorithm, and fast Fourier transforms.
Bialecki, B., Karageorghis, Andreas, Bialecki, B., Karageorghis, Andreas   +3 more
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Spectral analysis and spectral symbol of matrices in isogeometric collocation methods

Mathematics of Computation, 2015
We consider a linear full elliptic second order partial differential equation in a d d -dimensional domain,
Marco Donatelli, Carlo Garoni, Carla Manni, Stefano Serra-Capizzano, Hendrik Speleers   +4 more
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ADI spectral collocation methods for parabolic problems

Journal of Computational Physics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bernard Bialecki, Javier de Frutos
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Spectral Collocation on Triangular Elements

Journal of Computational Physics, 1998
Poisson problems on a segment of the unit disc and on triangles are considered. Using polar coordinates, the triangular elements are mapped on rectangular domains, where standard spectral collocation schemes are available. The authors employs a Chebyshev collocation method with Gauss-Labatto nodes in the polar coordinates.
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Hamilton–Pontryagin spectral-collocation methods for the orbit propagation

Acta Mechanica Sinica, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yi, Zhonggui, Yue, Baozeng, Deng, Mingle
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