A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

In this paper a numerical solution of one dimensional heat equation is presented using Galerkin B-spline finite element method. Quadratic B-spline basis functions are used for finding the solution. Two test problems are studied to evaluate the efficiency of the given technique. Numerical algorithms are developed for the simulation to hold. Results obtained are compared with the exact solution a...

In this paper, we construct a matrix, which transforms a generalized C-Bézier basis into a generalized uniform algebraic-trigonometric B-spline (C-B-spline or UAT B-spline) basis. We also show that it is a totally positive matrix and give a normalized B-basis of the generalized UAT B-splines.  2005 Elsevier B.V. All rights reserved.

The present paper studies adaptive refinement on multi-patch structures via the gluing approach. More precisely, we investigate the applicability of the gluing construction in isogeometric analysis on multi-patch domains with adaptively refined spline spaces. We will see that this is closely related to the concept of boundary compatibility of an adaptive spline construction. Given a spline basi...

For continuous probability density functions (PDFs) approximated by the B-spline basis functions, the relationships between the B-spline weights, the entropy and the mean have been analyzed in detail. It shows the different characteristics of the entropy with and without mean constraint. A minimum entropy controller subjected to mean constraint is developed by taking the performance function as...

In this paper one dimensional heat equation is solved using Galerkin B-spline Finite Element. Solution is obtained by reducing the initial boundary value problem to the set of Ordinary differential equations. Discretization of the spatial domain is made using cubic B-spline functions as basis functions. The numerical results obtained from the two test problems are compared with the analytical s...

We derive a new “convolution spline” approximation method for convolution Volterra integral equations. This shares some properties of convolution quadrature, but instead of being based on an underlying ODE solver is explicitly constructed in terms of basis functions which have compact support. At time step tn = nh > 0, the solution is approximated in a “backward time” manner in terms of basis f...

In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...