The aim of this paper is to carry out a rigorous error analysis for the Strang splitting Laguerre–Hermite/Hermite collocation methods for the time-dependent Gross–Pitaevskii equation (GPE). We derive error estimates for full discretizations of the three-dimensional GPE with cylindrical symmetry by the Strang splitting Laguerre–Hermite collocation method, and for the d-dimensional GPE by the Str...

In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size h. Based on this expansion,...

In this article we use discrete collocation method for solving Fredholm–Volterra integro– differential equations, because these kinds of integral equations are used in applied sciences and engineering such as models of epidemic diffusion, population dynamics, reaction–diffusion in small cells. Also the above integral equations with convolution kernel will be solved by discrete collocation metho...

will be employed in the analysis of the principle properties of the collocation approximations; the extension to nonlinear equations is straightforward (cf. [1, p. 225]). High-order numerical methods for VIDEs with weakly singular kernels may be found in [1,2,6,7,8]. In this note we shall consider collocation methods for VIDE (1.1), based on Brunner's approach [1]. The following method and nota...

In order to further research on the impact of collocations on readability, we have developed a software tool called ACFCalc. This tool calculates the Average Collocation Frequency for a sample text, based upon collocation frequency data from the sample text and from a reference corpus. The present paper describes the features of the ACFCalc application and details its requirements, in terms of ...

This paper reports on the development of a collocation extraction system that is designed within a commercial machine translation system in order to take advantage of the robust syntactic analysis that the system offers and to use this analysis to refine collocation extraction. Embedding the extraction system also addresses the need to provide information about the source language collocations ...

Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integrodifferential equation (VIDE) by polynomial spline functions. The polynomial spline collocation method is stable if all eigenvalues of a matrix are in the unit disk and all eigenvalues with |λ| = 1 belong to a 1× 1 Jordan block. Also many other conditions are derived depending u...

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

The collocation problem for noisy data with a piecewise constant noise variance is considered. An equivalence to the WIENERKOLMOGOROV equations in stationary collocation theory is constructed. A numerical solution based on HAAR wavelets is given.

The collocation of software development teams is common, especially in agile software development environments. However little is known about the impact of collocation on the team’s effectiveness. This paper explores the impact of collocating agile software development teams on a number of team effectiveness factors. The study focused on South African software development teams and gathered dat...