In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and comput...

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal this study use extended cubic B-spline (ExCuBS) functions with new second order derivative approximation obtain numerical solution weakly ...

Multi-degree Tchebycheffian splines are with pieces drawn from extended (complete) Tchebycheff spaces, which may differ interval to interval, and possibly of different dimensions. These a natural extension multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms so-called B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties ...

In this paper, we propose a fragment-based evaluation method for non-uniform B-spline surfaces using recent programmable graphics hardware (GPU). A position on a non-uniform Bspline surface is evaluated by the linear combination of both control points and B-spline basis functions. Hence the computational costs can be reduced by pre-computing a knot interval of a parameter from a knot vector. We...

A parametric class of modified B-spline functions is studied for its applicability in digital image interpolation tasks. The modified functions are generated by weighting and shifting of classical B-splines of different degrees. The weighting coefficients are optimized to assures an effective attenuation of the imaging frequencies, caused by the interpolation. The most computationally expensive...

This paper focuses on self-similar gravitational collapse solutions of the Einstein--axion-dilaton configuration for two conjugacy classes SL(2, R) transformations. These are invariant under spacetime dilation, combined with internal For first time in literature, we apply nonlinear statistical spline regression methods to estimate critical spherical black hole four dimension. include truncated ...

We construct a suitable normalized B-spline representation for C-continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are t...

Every m th order cardinal spline wavelet is a linear combination of the functions fN (l) m+l (2x?j); j 2 Zg. Here the function N m is the m th order cardinal B-spline. In this paper we prove that the single function N (l) m+l (2x), or N (l) m+l (2x ? 1) is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases, the smoothness of...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

The construction of classical hierarchical B–splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only decreases the overlapping of supports ...