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Collocation Methods for Integro-Differential Equations
SIAM Journal on Numerical Analysis, 1977In this note we extend the work of de Boor and Swartz (SIAM J. Numer. Anal., 10 (1973), pp. 582-606) on the solution of two-point boundary value problems by collocation. In particular, we are concerned with boundary value problems described by integro-differential equations involving derivatives of order up to and including m with m boundary conditions.
Hangelbroek, Rutger J. +2 more
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Random Collocation Method (RCM)
Volume 7: CFD and VIV; Offshore Geotechnics, 2010Recently, young people do not show much interest on theory, and a lack of communication is occurring between the older and younger generations. This tells us that a much simpler numerical procedure directly related to the governing equations is strongly required and the effort answering the requirement should be continued.
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Communications in Applied Numerical Methods, 1985
AbstractThe upwind collocation method is analysed in a way which clearly demonstrates its similarities to other upwind schemes. The dispersion detected by Dougherty and Pinder5 is shown to be of little significance to the quality of the approximation.
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AbstractThe upwind collocation method is analysed in a way which clearly demonstrates its similarities to other upwind schemes. The dispersion detected by Dougherty and Pinder5 is shown to be of little significance to the quality of the approximation.
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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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Collocation and Collocation-Quadrature Methods for Strongly Singular Integral Equations
2021In this chapter collocation and collocation-quadrature methods, based on some interpolation and quadrature processes considered in Chap. 3, are applied to strongly singular integral equations like linear and nonlinear Cauchy singular integral equations, integral equations with strongly fixed singularities, and hypersingular integral equations.
Peter Junghanns +2 more
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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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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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C0 — Collocation — Galerkin methods
1979A C0-Collocation-Galerkin (C0-C-G) method is formulated and analyzed for finite element solution of linear and nonlinear singular boundary-value problems. Theoretical error estimates are ascertained for both the linear problems and a specific class of nonlinear problems.
G. F. Carey, M. F. Wheeler
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The basis-spline collocation method
AIP Conference Proceedings, 1995We outline the main features of the basis‐spline collocation method used for the lattice discretization of boundary‐value differential systems. We demonstrate the implementation of a general set of boundary conditions. The spectral properties of derivative operators are also discussed.
A. S. Umar, J. C. Wells, M. R. Strayer
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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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