Results 241 to 250 of about 12,633,357 (288)

Collocation methods: More efficient procedures for applying collocation

Advances in Engineering Software, 2007
In recent years, new and more effective procedures for applying collocation have been published. This article is devoted to present a revision of this subject and complement its developments. From the general theory two broad approaches are derived, which yield the direct and the indirect TH-collocation methods.
Ismael Herrera, Robert Yates, Ernesto Rubio   +2 more
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Collocation methods for Poisson’s equation

Computer Methods in Applied Mechanics and Engineering, 2006
The main feature of the present paper is that the collocation method is treated as the least squares method involving integration approximation. Dirichlet, Neumann and Robin boundary value problems are considered. Based on integration approximation, the authors locate not only the collocation nodes, but they are also concerned with the error analysis ...
Hu, Hsin-Yun, Li, Zi-Cai
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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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A dual method to the collocation method

Mathematical Methods in the Applied Sciences, 1988
AbstractIn this article we consider methods which are related to the collocation method by interchanging the test and the trial spaces. Error estimates are derived. As a by‐product we obtain some extensions to the known convergence results for the collocation method.
Ruotsalainen, K., Saranen, J.
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C0 — Collocation — Galerkin methods

1979
A 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.
Graham F. Carey, Mary F. Wheeler
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Generalized Collocation Methods

2008
This book has been proposed to offer engineers and scientists various mathematical tools, based on generalized collocation methods, to solve nonlinear problems related to partial differential and integro-differential equations.
BELLOMO, Nicola, LODS B, REVELLI, Roberto, RIDOLFI, LUCA   +3 more
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Galerkin and Collocation Methods

2018
One 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, Victo dos Santos Filho, Thiago Carvalho Peixoto   +2 more
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Atom collocation method

Computer Methods in Applied Mechanics and Engineering, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Qingcheng, Biyikli, Emre, Zhang, Pu, Tian, Rong, To, Albert C.   +4 more
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Superconvergence of a Chebyshev Spectral Collocation Method

Journal of Scientific Computing, 2007
A 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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Collocation Methods for Integro-Differential Equations

SIAM Journal on Numerical Analysis, 1977
In 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., Kaper, Hans G., Leaf, Gary K.   +2 more
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