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A dual method to the collocation method
Mathematical Methods in the Applied Sciences, 1988AbstractIn 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.
Keijo Ruotsalainen, J. Saranen
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Collocation methods for distillation design.
1995Abstract: "Fast and accurate distillation design requires a model that significantly reduces the problem size while accurately approximating a full order distillation column model. Variable number of trays and variable feed tray location make optimization possible.
Huss, Robert S. +1 more
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Collocation methods for Poisson’s equation [PDF]
Computer Methods in Applied Mechanics and Engineering, 2006 Abstract In this paper, we provide an analysis on the collocation methods (CM), which uses a large scale of admissible functions such as orthogonal polynomials, trigonometric functions, radial basis functions and particular solutions, etc. The admissible functions can be chosen to be piecewise, i.e., different functions are used in different ...
Zi-Citi Li, Zi-Citi Li, Hsin-Yun Hu
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Computer Methods in Applied Mechanics and Engineering, 2012
This paper presents a new concurrent atomistic-continuum method called the atom collocation method (ACM). By adopting the framework of continuum collocation method, ACM aims at overcoming the current difficulties in interfacial mismatch, adaptive analysis, and parallel implementation of existing atomistic-continuum methods.
Emre Biyikli +4 more
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This paper presents a new concurrent atomistic-continuum method called the atom collocation method (ACM). By adopting the framework of continuum collocation method, ACM aims at overcoming the current difficulties in interfacial mismatch, adaptive analysis, and parallel implementation of existing atomistic-continuum methods.
Emre Biyikli +4 more
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Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients
SIAM/ASA J. Uncertain. Quantification, 2016We evaluate the performance of global stochastic collocation methods for solving nonlinear parabolic and elliptic problems (e.g., transient and steady nonlinear diffusion) with random coefficients.
D. Barajas-Solano, D. Tartakovsky
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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.
Thiago Carvalho Peixoto +2 more
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SIAM Journal on Scientific Computing, 2016
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements.
M. Parsani +3 more
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Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements.
M. Parsani +3 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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