In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This is based on basis functions with for the second-order derivative. The theoretical derivative and error analysis have been successfully derived. We found that was O(h3) accurate. By using approximation, proposed O(h5) Four numerical consisting of ordinary dif...

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been pr...

Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while second DQM. resulting system of ODEs solved by SSP RK43 method after aforementioned spatially discretized. To assess success chosen tactics, a comparison errors shown. graphs can...

7. The Case of Periodic Data.-In a recent paper5 I introduced the method of trigonometric spline interpolation. The discussion of sections 4 and 5 carries over to the periodic case and need not be elaborated. The analogue of Problem 1 is as follows: assuming 2m + 2 < n, e > 0, we are seeking the function f(x), of period 2 r, having a square integrable (2m + 1)st derivative and which solves the ...

Tchebycheffian splines are smooth piecewise functions whose pieces drawn from (possibly different) Tchebycheff spaces, a natural generalization of algebraic polynomial spaces. They enjoy most the properties known in spline case. In particular, under suitable assumptions, admit representation terms basis functions, called B-splines (TB-splines), completely analogous to B-splines. A particularly ...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...

Best L1 approximations of the Heaviside function in Chebyshev and weak-Chebyshev spaces has a Gibbs phenomenon. It has been shown in the nineties for the trigonometric polynomial [1] and polygonal line cases [2]. By mean of recent results of characterization of best L1 approximation in Chebyshev and weak-Chebyshev spaces [3] that we recall, this Gibbs phenomenon can also be evidenced in the pol...