In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [14] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also disc...

â  â  â  reasons of differences in grammatical opinions among the ancients â â â â â â â  ryadh alsawad * â  marzieh ghorbankhani ** â  â  abstract â â â  the most important characteristic of the rules of arabic language is their extent and diversity, so that they are difficult for learners to manage and learn. there are different reasons that play role in formation of this diversity. some reas...

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 paper presents an annotated Chinese collocation bank developed at the Hong Kong Polytechnic University. The definition of collocation with good linguistic consistency and good computational operability is first discussed and the properties of collocations are then presented. Secondly, based on the combination of different properties, collocations are classified into four types. Thirdly, th...

In recent years, collocation has been widely acknowledged as an essential characteristic to distinguish native speakers from non-native speakers. Research on academic writing has also shown that collocations are not only common but serve a particularly important discourse function within the academic community. In our study, we propose a machine learning approach to implementing an online collo...

A numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral collocation method is presented in this article. A Chebyshev-Gauss-Radau collocation (C-GR-C) method in combination with the implicit RungeKutta scheme are employed to obtain highly accurate approximations to the mentioned problem. The collocation points are the Chebyshev interpolation n...

Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and op...