We address the problem of automatically processing collocations—a subclass of multi-word expressions characterized by a high degree of morphosyntactic flexibility—in the context of two major applications, namely, syntactic parsing and machine transla...
Collocations typically refer to habitual word combinations, which not only occur in texts but also constitute an essential component of the mental lexicon. This study focuses on the mental lexicon of Chinese learners of English as a foreign language...
Accurate atmospheric 3D wind observations are one of the top priorities for the global scientific community. To address this requirement, and to support researchers’ needs to acquire and analyze wind data from multiple sources, the System for A...
This study investigated the effectiveness, as well as EFL learners’ perceptions, of the keyword method (KWM) in comparison to the rote learning method (RLM) for the learning of English collocations. A controlled laboratory-like setting was adop...
This article explores patterns of linguistic behaviour and challenges associated with low(er) linguistic competences in primary school learners in subject-specific areas of the curriculum. The study draws on science test data, specifically on two ass...
Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin and collocation formulations. Exploi...
In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomia...
This study examines the influence of Tamil (L1) on the processing of English (L2) collocations during reading for Tamil-English bilingual children. Building on existing research in formulaic language, we used an online processing tool to investigate...
The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for...
In this study, a collocation method based on Bernstein polynomials is developed for solution of the nonlinear ordinary differential equations with variable coefficients, under the mixed conditions. These equations are expressed as linear ordinary dif...
This paper is concerned with collocation methods for one class of impulsive delay differential equations (IDDEs). Some results for the convergence, global superconvergence and local superconvergence of collocation methods are given. We choose a suita...
In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points He...
This systematic review critically examines 32 previous empirical studies on corpus-based collocation acquisition and learning in EFL contexts, aiming to identify the research contexts, corpus types, instructional methods, and how corpus-based trainin...
The primary issue in developing hexapod robots is generating legged motion without tumbling. However, when the hexapod is designed with collocated actuators, where each joint is directly mounted with an actuator, the number of actuators is usually hi...
Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. In this paper, we present a spectral collocation method with tempered fractional Jacobi functions (TFJFs) as basis functions and obtain an efficient algorithm t...
This paper presents a collocation method for the approximate solution of two-dimensional mixed Volterra–Fredholm integral equations of the Hammerstein type. For a reformulation of the equation, we consider the domain of integration as a planar...
Flexoelectricity is an electromechanical coupling between the electric field and the mechanical strain gradient, as well as between the mechanical strains and the electric field gradient, observed in all dielectric materials, including those with cen...
The highly oscillatory algebraic singular Volterra integral equations cannot be solved directly. A collocation numerical method is proposed to overcome the difficulty created by the highly oscillatory algebraic singular kernel. This paper is composed...
This study presents a new method for the solution of mth-order linear differential-difference equations with variable coefficients under the mixed conditions. We introduce a Fibonacci collocation method based on the Fibonacci polynomials for the appr...
The accuracy and consistency of a quintuple collocation analysis of ocean surface vector winds from buoys, scatterometers, and NWP forecasts is established. A new solution method is introduced for the general multiple collocation problem formulated i...
We present a collection of recent results on the numerical approximation of Volterra integral equations and integro-differential equations by means of collocation type methods, which are able to provide better balances between accuracy and stability...
A numerical solution of the Equal Width (EW) equation based on a collocation method incorporated cubic B-splines is investigated. Accuracy of the proposed method is shown numerically by calculating conservation laws, L2 and L∞ norms on studying migra...
The automatic construction of learners’ dictionaries requires robust methods for identifying non-literal word combinations, or collocations, which represent a significant challenge for second-language (L2) learners. This paper addresses the cri...
This paper proposes a Chebyshev spectral collocation method for nonlinear Volterra–Hammerstein integral equations of the second kind with smooth kernels. We approximate the unknown solution using a finite Chebyshev expansion and place collocati...
Triple collocation analysis is an established technique for calculating the relative linear intercalibration coefficients and observation error variances for physical quantities measured simultaneously in space and time by three different observation...
We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions...
A dynamical system is a particle or set of particles whose state changes over time. The dynamics of the system is described by a set of differential equations. If the derivatives involved are of non-integer order, we obtain a fractional dynamical sys...
In this study, a finite-volume computational fluid dynamics (CFD) technique for application on skewed meshes using staggered pressure nodes is proposed. The method is based on the derivation of a momentum equation for the cell face velocities from ap...
The recognition that collocation is an important, yet challenging, variable in second language development has attracted extensive research into how to enhance collocation learning. This study examines the collocational knowledge of Libyan Arabic-spe...
The multigroup neutron diffusion criticality problem is studied by the radial basis function collocation method. The multiquadric is chosen as the radial basis function. To investigate the effectiveness of the method, one, two and three-group problem...
The isogeometric collocation method (IGA-C), which is a promising branch of isogeometric analysis (IGA), can be considered fitting the load function with the combination of the numerical solution and its derivatives. In this study, we develop an iter...
In this article, the nonlinear heat equilibrium problems are solved by the local multiquadric (MQ) radial basis function (RBF) collocation method. The system of nonlinear algebraic equations is solved by iteration based on the residual norm-based alg...
Given the fact that Cross-track Infrared Sounder (CrIS) and the Visible Infrared Imaging Radiometer Suite (VIIRS) are currently onboard the Suomi National Polar-orbiting Partnership (Suomi NPP) satellite and will continue to be carried on the same pl...
In this paper, a collocation method based on the Jacobi polynomial is proposed for a class of optimal-control problems of a fractional distributed system. By using the Lagrange multiplier technique and fractional variational principle, the stated pro...
In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form. The...
The stochastic collocation method for solving differential equations with random inputs has gained lots of popularity in many applications, since such a scheme exhibits exponential convergence with smooth solutions in the random space. However, in so...
This review considers piecewise polynomial functions, that have long been known to be a useful and versatile tool in numerical analysis, for solving problems which have solutions with irregular features, such as steep gradients and oscillatory behavi...
In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach ena...
An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs). To do this, we reduce the desired equation to an equivalent linear or nonlinear...
The main focus in this manuscript is to find a numerical solution of a dengue fever disease model by using the Fibonacci wavelet method. The operational matrix of integration has been obtained using Fibonacci wavelets. The proposed method is called F...
This work is about the use of some classical spectral collocation methods as well as with the new software system Chebfun in order to compute the eigenpairs of some high order Sturm–Liouville eigenproblems. The analysis is divided into two distinct d...
In this work, an alternate Schwarz domain decomposition method is proposed to solve a Rayleigh–Bénard problem. The problem is modeled with the incompressible Navier–Stokes equations coupled with a heat equation in a rectangular dom...
In this article, a novel infinitely smooth polyharmonic radial basis function (PRBF) collocation method for solving elliptic partial differential equations (PDEs) is presented. The PRBF with natural logarithm is a piecewise smooth function in the con...
The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The...
We propose a wavelet collocation method for solving the fractional Riccati equation, using the Müntz–Legendre wavelet basis and its associated operational matrix of fractional integration. The fractional Riccati equation is first transform...
Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research. Volume penalization techniques allow complex immersed boundary conditions to be used with high efficiency...
In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from...
Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height (SWH). Traditionally, validation of SAR derived SWH has been carried out against buoy measurements or model outputs, which only yield...
This paper investigates the spatial and temporal variability of significant wave height (Hs) and wind speed (U10) using altimeter data from the Australian Ocean Data Network (AODN) and buoy data from the National Data Buoy Center (NDBC). The main goa...
Searching names of persons, families, and organizations is often difficult in online databases because different persons or organizations frequently share the same name and because a single person’s or organization’s name may appear in different form...
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