Gibbs phenomenon is the particular manner how a global spectral approximation of a piecewise analytic function behaves at the jump discontinuity. The truncated spectral series has large oscillations near the jump, and the overshoot does not decay as the number of terms in the truncated series increases. There is therefore no convergence in the maximum norm, and convergence in smooth regions awa...

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

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 a numerical technique is presented for the solution of fuzzy linear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions(RBFs).We first solve the actual set are equivalent to the fuzzy set, then answer 1-cut into the equation. Also high convergence rates and good accuracy are obtain with the propose method ...

A collocation-Galerkin method is defined for Poisson's equation on the unit 2 square, using tensor products of continuous piecewise polynomials. Optimal L and Hq orders of convergence are established. This procedure requires fewer quadratures than the corresponding Galerkin procedure. Introduction. The collocation-Galerkin method was first introduced by Diaz [2], [3] for the two-point boundary ...

In this paper we present KX, a system for keyphrase extraction developed at FBK-IRST, which exploits basic linguistic annotation combined with simple statistical measures to select a list of weighted keywords from a document. The system is flexible in that it offers to the user the possibility of setting parameters such as frequency thresholds for collocation extraction and indicators for keyph...

We use the visualization and animation capabilities of Maple throughout our courses. Animations are used in presentations in class from first year onwards. For example, animations for Newton’s method and for fixed point iteration; to illustrate how slicing is used to generate the domain for double integration; to show how the error function (for the collocation method solution of a boundary val...

In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important ...