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Computer Methods in Applied Mechanics and Engineering, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Qingcheng +4 more
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Yang, Qingcheng +4 more
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Collocation methods for Poisson’s equation
Computer Methods in Applied Mechanics and Engineering, 2006The 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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Least‐squares collocation meshless method
International Journal for Numerical Methods in Engineering, 2001AbstractA finite point method, least‐squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satisfied not only at the collocation points but also at the ...
Zhang, Xiong +3 more
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Semi-implicit multivalue almost collocation methods
AIP Conference Proceedings, 2022We propose a family of multivalue collocation methods for the numerical solution of differential problems, potentially candidate to be stiff. For this reason, the suggested numerical schemes have strong stability properties, such as A-stability. Moreover, in order to obtain an efficient implementation, it is desirable to impose the conditions gaining a
Dajana Conte +3 more
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Collocation methods: More efficient procedures for applying collocation
Advances in Engineering Software, 2007In 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 +2 more
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Fractional Spectral Collocation Method
SIAM Journal on Scientific Computing, 2014We 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 Em Karniadakis
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Generalized Collocation Methods
2008This 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 +3 more
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The variational collocation method
Computer Methods in Applied Mechanics and Engineering, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hector Gomez, Laura De Lorenzis
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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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