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Galerkin and Collocation Methods
2018One method to numerically solve an equation consists in expanding the solution in terms of a set of known basis functions. These are the so-called “spectral” methods, where the main emphasis is placed on establishing procedures to obtain the expansion coefficients.
George Rawitscher +2 more
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Spectral collocation methods for polymer brushes
The Journal of Chemical Physics, 2011We 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 +4 more
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An extended collocation method
Calcolo, 1980Given an approximate solutionxn of a linear operator equation obtained by a collocation method, an improved solutionx*n+m is obtained fromxn by an «extended collocation method» which consists in solving a further (m)-order linear system instead of an (n+m)-order one, diminishing the effects of rounding error in carrying out the calculations.
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The Laguerre Collocation Method
2014The chapter introduces first the functional framework corresponding to the spectral collocation method based on Laguerre functions. The main advantage of these functions is the fact that they decrease smoothly to zero at infinity along with their derivatives. We speculate this behavior in imposing boundary conditions at large distances.
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The Multigrid Iteration Applied to the Collocation Method
SIAM Journal on Numerical Analysis, 1981We describe an application of the multigrid iteration to the collocation approximation for elliptic equations using a bicubic Hermite basis. A block relaxation and a projection operator specific to the collocation approximation were required to obtain convergence.
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2018
Collocation method involves numerical operators acting on point values (collocation points) in the physical space. Generally, wavelet collocation methods are created by choosing a wavelet and some kind of grid structure which will be computationally adapted.
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Collocation method involves numerical operators acting on point values (collocation points) in the physical space. Generally, wavelet collocation methods are created by choosing a wavelet and some kind of grid structure which will be computationally adapted.
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Perturbed collocation and symplectic RKN methods
Advances in Computational Mathematics, 1995It is shown that, within the class of Runge-Kutta-Nyström collocation methods, only the method of maximal order \(p = 2s\) is symplectic. By extending the idea of perturbed collocation proposed by \textit{S. P. Nørsett} and \textit{G. Wanner} [Numer. Math.
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The Chebyshev Collocation Method
2014The chapter is devoted to the efficient implementation of Chebyshev collocation method. First, the performances of the method in solving fourth order GEPs are compared with those of ChT and ChG counterparts. Then, ChC method is used to solve some genuinely high order, i.e., larger than two, and/or singularly perturbed eigenvalue problems.
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Immersed isogeometric analysis based on a hybrid collocation/finite cell method
Computer Methods in Applied Mechanics and Engineering, 2023Michele Torre +2 more
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