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.

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...