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

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower deg...

We 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. We perform such a construction following a spectral theory recently developed in [M. Zayernouri ...

We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text]...