In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.

In the present paper, we discuss three point difference method based on nonpolynomial spline basis for the second order ordinary differential equation. Difference schemes are derived for linear and nonlinear case and are used to solve via two parameter alternating group explicit iterative algorithm. The schemes have a fourth and second order of uniform convergence for the choice of the paramete...

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree...

The objective of this paper is to provide an ef®cient and reliable algorithm for representing and evaluating the boundary of the interval Be Âzier curve in 2-and 3-D. The boundary of the planar Be Âzier curve is represented by a sequence of Be Âzier curve segments with same degree and line segments in the order they are encountered when marching counterclockwise along its boundary. The boundary...

T-spline has been recently developed to represent objects of arbitrary shapes using a smaller number of control points than the conventional NURBS or B-spline representations in computer aided design, computer graphics, and reverse engineering. However, existing methods for fitting a T-spline over a point cloud are slow. By shifting away from the conventional iterative fitand-refine paradigm, w...

N-dimensional surfaces are defined by the tensor product of B-spline basis functions. To estimate the unknown control points of these B-spline surfaces, the lofting method also called skinning method by cross-sectional curve fits is applied. It is shown by an analytical proof and numerically confirmed by the example of a four-dimensional surface that the results of the lofting method agree with...

A simple and elegant method is presented to perform anti-aliasing in computer-generated images. The method uses stratified sampling to reduce the occurrence of artifacts in the image and features a B-spline filter, of some desired order, to compute the final luminous intensity at each pixel. The method is scalable through the specification of the filter order. A B-spline filter of order one amo...

A new differential quadrature method based on quartic B-spline functions is introduced. The weighting coefficients are determined via a semi-explicit algorithm containing an algebraic equation system with four-band coefficient matrix. In order to validate the proposed method, the Burgers’ Equation is selected as test problem. The shock wave and the sinusoidal disturbance solutions of the Burger...

We propose a lag selection method for nonlinear additive autoregressive models based on spline estimation and the BIC criterion. The additive structure of the autoregression function is used to overcome the “curse of dimensionality”, while the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the proposed method. Compr...