Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the sinc-collocation method for solving linear and nonlinear system of second order differential equation. The method is then tested on linear and nonlinear examples and a comparison with B-spline method is made. It i...

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell’s equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fiel...

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

We investigate collocation methods for the efficient solution of singular boundary value problems with an essential singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to...

The stochastic collocation method [43, 1, 31, 30] has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method [28, 40, 33], primarily developed for solving parametric systems, has been recently used to deal with stochastic problems [7, 6]. In this work, we aim at comparing the performance of the two methods when applied t...

The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems and partial differential equations despite the lack of theoretical support. The simple leastsquares (LS) formulation, on the other hand, makes the study of its solvability and convergence rather nontrivial. In this p...

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...

We present an experiment in extracting collocations from the FrameNet corpus, specifically, support verbs such as direct in Environmentalists directed strong criticism at world leaders. Support verbs do not contribute meaning of their own and the meaning of the construction is provided by the noun; the recognition of support verbs is thus useful in text understanding. Having access to a list of...

We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semiinfinite domain x ∈ 0,∞ onto a half-open interval t ∈ −1, 1 . The resulting finite-domain twopoint boundary value problem is transcribed to a system of algebraic equations using ChebyshevGauss CG collocation, wh...