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LEAST-SQUARES MESHFREE COLLOCATION METHOD
International Journal of Computational Methods, 2012A least-squares meshfree collocation method is presented. The method is based on the first-order differential equations in order to result in a better conditioned linear algebraic equations, and to obtain the primary variables (displacements) and the dual variables (stresses) simultaneously with the same accuracy.
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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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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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