In this paper, a well-conditioned collocation method is constructed for solving general p-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the n...

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

This article investigates the stability of the collocation method for the Radiosity equation. We introduce graded meshes and trial spaces of piecewise poynomials and prove stability for some modified collocation method. Next we show that graded meshes are necessary, even for linear convergence. The generation of triangulations which allow higher order approximations leads to geometrical problem...

This study evaluates the impact of integrating two different collocation segmentations methods in a standard phrase-based statistical machine translation approach. The collocation segmentation techniques are implemented simultaneously in the source and target side. Each resulting collocation segmentation is used to extract translation units. Experiments are reported in the English-to-Spanish Bi...

Collocation and colligation are two closely related concepts associated with the distributional properties of linguistic items in actual language use. Specifically, collocation and colligation refer to the likelihood of co-occurrence of (two or more) lexical items and grammatical categories, respectively. Both terms have been attributed to J. R. Firth (1957: 194–195; 1968: 181–183; see Östman a...

‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

: This study investigated the impact of audio-visual input enhancement teaching techniques on improving English as Foreign Language (EFL) learnersˈ collocation learning as well as their accuracy concerning collocation use in narrative writing. In addition, it compared the impact and efficiency of audio-visual input enhancement in two learning contexts, namely traditional and mo...

The von-K arm an nonlinear, dynamic, partial differential system over rectangular domains is considered, and numerically solved using both the Chebyshev-collocation and Legendre-collocation methods for the spatial discretization and the implicit Newmark-b scheme combined with a non-linear fixed point algorithm for the temporal discretization. As the system is non-linear, involving operators of ...

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic ...