The one dimensional Burgers' equation is solved numerically using a finite element method, where a combination of cubic B-splines is used as an approximating function. Different comparisons for the test problem in hand, are made to validate the proposed numerical technique. Results obtained from the proposed numerical scheme are found to be in good agreement with the exact solution.

This paper describes a simple and efficient non-stationary subdivision scheme of order 4. This curve scheme unifies known subdivision rules for cubic B-splines, splines-in-tension and a certain class of trigonometric splines capable of reproducing circles. The curves generated by this unified subdivision scheme are C2 splines whose segments are either polynomial, hyperbolic or trigonometric fun...

BACKGROUND Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS We compared several meth...

This paper discusses a method of modelling collisions between long hairs. The hairs are modelled as cubic B-splines, to which chains of cylinders are fitted for the purposes of collision detection. The head on which the hairs rest is modelled as an ellipsoid. The paper explains how to fit cylinder chains to splines, how to test whether and where two cylinder chains intersect, and how to test wh...

Sometimes, the relationship between an outcome (dependent) variable and the explanatory (independent) variable(s) is not linear. Restricted cubic splines are a way of testing the hypothesis that the relationship is not linear or summarizing a relationship that is too non-linear to be usefully summarized by a linear relationship. Restricted cubic splines are just a transformation of an independe...

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are computed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. Exact estimations of th...

The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consisten...

This paper is an overview of three spline approaches of degree one, two and three. It represents the review and comparative study of Linear, conic and cubic splines for the vectorization of outlines of the planar images. It has various phases including extracting outlines of images, detecting corner points from the detected outlines, and curve fitting. The idea of simulated annealing has been i...

A trivariate Lagrange interpolation method based on C1 cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.