The appropriate use of collocations is a challenge for second language acquisition. However, high quality and easily accessible Chinese collocation resources are not available for both teachers and students. This paper presents the design and construction of a large scale resource of Chinese collocational knowledge, and a web-based application (OCCA, Online Chinese Collocation Assistant) which ...

A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H2-norm error estimate is obtained for th...

This work proposes and analyzes a sparse grid stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms (input data of the model). This method can be viewed as an extension of the Stochastic Collocation method proposed in [Babuška-Nobile-Tempone, Technical report, MOX, Dipartimento di Matematica, 2005] which consists of a Galerk...

The problem of solving pseudodiierential equations on spheres by collocation with zonal kernels is considered and bounds for the approximation error are established. The bounds are given in terms of the maximum separation distance of the collocation points, the order of the pseudodiierential operator, and the smoothness of the employed zonal kernel. A by-product of the results is an improvement...

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

The Fourier pseudo-spectral method has been studied for a onedimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of convergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of the second problem obtained by the present meth...

in this paper, we propose a new numerical method for solution of urysohn two dimensional mixed volterra-fredholm integral equations of the second kind on a non-rectangular domain. the method approximates the solution by the discrete collocation method based on inverse multiquadric radialbasis functions (rbfs) constructed on a set of disordered data. the method is a meshless method, because it i...

Closed-form algebraic formulae are derived for the local error incurred in the numerical solution of integral equations by iterated collocation methods, the analysis being illustrated by application to Fredholm integral equations of the second kind. The novel error analysis uses an asymptotic approach, in the small parameter of the numerical mesh size, applied to a finite-rank degenerate-kernel...