In this paper, we consider the development of an extended block integrator for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using interpolation and collocation techniques. The integrator was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (...

This paper presents the design and construction of an annotated Chinese collocation bank as the resource to support systematic research on Chinese collocations. With the help of computational tools, the bi-gram and n-gram collocations corresponding to 3,643 headwords are manually identified. Furthermore, annotations for bi-gram collocations include dependency relation, chunking relation and cla...

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...

Studies on language learning have revealed that collocation knowledge is an important indicator for advanced second language competence. Native speakers' production relies heavily on prefabricated or pre-made chunks such as collocations, which save processing load to achieve language fluency and accuracy. Previous investigation on ESL and EFL students indicated that nonnative learners' collocat...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving non-linear Troesch’s problem. In first approach, by expressing unknown solution and its second derivative in terms of matrix form along with some collocation points, governing equation transforms into a algebraic equation. technique quasi-linearization is employed to linea...

A wavelet is a basis function used to construct a wavelet transform. The first known wavelet – Haar wavelet was proposed in 1909 by Alfred Haar. Wavelet theory has been applied to various problems including signal processing in communications, image compression-extraction, solution of the linear and nonlinear integral equations etc. Haar wavelet based discretization technique is adopted for sol...

In this paper, the orthogonal collocation technique is utilized to solve the Poppe method equations for heat and mass transfer in counter flowing wet-cooling towers. The six differential equations for unsaturated and supersaturated air from the Poppe method are simplified, yielding three differential equations that use the Heaviside function. The humidity ratio is demonstrated to be a finite po...

In this paper, we have proposed a Haar wavelet quasilinearization method to solve the well known Blasius equation. The method is based on the uniform Haar wavelet operational matrix defined over the interval [0, 1]. In this method, we have proposed the transformation for converting the problem on a fixed computational domain. The Blasius equation arises in the various boundary layer problems of...