Convergence analysis of nite-diierence approximations of an inhomogeneous singularly perturbed boundary value problem using grid equidistribution. We derive-uniform error estimates for two rst-order upwind discretisations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, is the small parameter multiplying the highest derivative term...

This work presents the convergence of the cell average technique (J. Kumar et al., 2007, Powder Technology 179, 205-228) for solving breakage population balance equation. Similarly to our paper Kumar and Warnecke [5] of this series, we study convergence on four different types of meshes. A second order convergence is proved for uniform, locally uniform and non-uniform smooth meshes. Finally the...

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem. We study uniform convergence properties of the AUC; in particular, we derive a distribution-free uniform convergence bound for the AUC which serves to bound the expected accuracy of a learned ranking function in terms of its empirical AUC on the training sequence from which it is ...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

We consider the convergence problem of autonomous mobile robots with inaccurate sensors, which may return the erroneous location of other robots. In this paper, we newly introduce a uniform error model, which is a restricted variant of the original observation-error model proposed by Cohen and Peleg [4]. The degree of an observation error is characterized by distance errors and angle errors. Wh...

In [5] Lenz and Stollmann proved the existence of the integrated density of states in the sense of uniform convergence of the distributions for certain operators with aperiodic order. The goal of this paper is to establish a relation between aperiodic order, uniform spectral convergence and the continuous algebras invented by John von Neumann. We illustrate the technique by proving the uniform ...

This paper presents stability and convergence analysis of a finite volume scheme (FVS) for solving aggregation, breakage and the combined processes by showing Lipschitz continuity of the numerical fluxes. It is shown that the FVS is second order convergent independently of the meshes for pure breakage problem while for pure aggregation and coupled equations, it shows second order convergent on ...