In this paper, we propose a natural collocation method with exact imposition of mixed boundary conditions based on a generalized Gauss-Lobatto-Legendre-Birhoff quadrature rule that builds in the underlying boundary data. We provide a direct construction of the quadrature rule, and show that the collocation method can be implemented as efficiently as the usual collocation scheme for PDEs with Di...

This work presents an initial investigation on how to distinguish collocations from free combinations. The assumption is that , while free combinations can be literally translated, the overall meaning of collocations is different from the sum of the translation of its parts. Based on that, we verify whether a machine translation system can help us perform such distinction. Results show that it ...

A collocation method is presented for numerical solution of a typical integral equation Rh := R D R(x, y)h(y)dy = f(x), x ∈ D of the class R, whose kernels are of positive rational functions of arbitrary selfadjoint elliptic operators defined in the whole space R, and D ⊂ R is a bounded domain. Several numerical examples are given to demonstrate the efficiency and stability of the proposed meth...

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

We present a collocatIon method based on piecewise cubic polynomials I In C for solving various Integral and differential equatIons. Two new methods for handling curved boundaries are discussed based on collocation and discrete least-squares. Finally, a summary of the properties of the collocation method Is given which IndIcates the simplicity, flexlbl1fty, efficiency, and generality of the met...

In this paper we present a new method of automatic collocation identification. Collocation is an important relation between words, which is widely used, among others, in information retrieval tasks. Over the last years, many methods of automatic collocation acquisition from text corpora have been proposed. The approach described in this paper differs from the others by focusing on domain colloc...

This paper describes the use of WordNet in a new technique for collocation extraction. The approach is based on restrictions on the possible substitutions for synonyms within candidate phrases. Following a general discussion of collocations and their applications, current extraction methods are briefly described. This is followed by a detailed description of the new approach and results and eva...

Article history: Received 15 December 2010 Received in revised form 21 April 2011 Accepted 24 April 2011 Available online 4 May 2011