In this paper we propose a convergence acceleration method for collocation solutions of the linear second-kind Volterra integral equations with proportional delay qt (0 < q < 1). This convergence acceleration method called multilevel correction method is based on a kind of hybrid mesh, which can be viewed as a combination between the geometric meshes and the uniform meshes. It will be shown tha...

The exponentially weighted moving average chart of the squared deviation (EWMAS) is often applied for monitoring changes such as step shifts and linear drifts in process variation when no subgrouping is available. This paper analyzes the performance of the EWMAS chart under drifts in process variation. A fast and accurate algorithm based on the piecewise collocation method is presented for comp...

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.

Let the parabolic problem cix, t, u)ut = aix, t, u)uxx + bix, t, u, ux), 0 < x < 1, 0 < / á T, uix, 0) = fix), w(0, t) = gli), ií(1, t) = giit), be solved approximately by the continuous-time collocation process based on having the differential equation satisfied at Gaussian points £,,i and £;,2 in subintervals (x,-_i, x¡) for a function l/:[0, T] —» 3C3, the class of Hermite piecewise-cubic po...

This paper is concerned with error estimates for the numerical solution of linear ordinary differential equations by global or piecewise polynomial collocation which are based on consideration of the differential operator involved and related matrices and on the residual. It is shown that a significant advantage may be obtained by considering the form of the residual rather than just its norm.

In tuple space approaches to context-aware mobile systems, the notion of context is defined by the presence or absence of certain tuples in the tuple space. Existing approaches define such presence either by collocation of devices holding the tuples or by replication of tuples across all devices. We show that both approaches can lead to an erroneous perception of context. Collocation ties the p...

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium in non-periodic space. The concentration is treated by a characteristics collocation method, while the pressure is treated by a finite element collocation method. Optimal order estimates in L2 is derived.

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...

In this paper, we will present a review of the multistep collocation method for Delay Volterra Integral Equations (DVIEs) from [1] and then, we study the superconvergence analysis of the multistep collocation method for DVIEs. Some numerical examples are given to confirm our theoretical results.