In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k) as h → 0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k = 1, 2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polyn...

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the newmethod are given and the efficiency of the newmethod is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-or...

In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One these equations, dissipative wave equation, has found a plethora useful applications different fields. A special class solutions studied for equation including exact approximate solutions. The...

For planar spline curves and bivariate box-spline functions, the cone of normals of a polynomial spline piece is enclosed by the cone of normals of its spline control polyhedron. This note collects some concrete examples to show that this is not true for subdivision surfaces, both at extraordinary points and in the regular, box-spline setting. A larger set, the cross products of families of con...

We consider the self-adjoint singularly perturbed two-point boundary value problems. We know that the numerical methods for solution of such problems based on nonpolynomial spline in grid points, can produce the fourth order method only. So that we look for an alternative to obtain higher order methods. We develop the non-polynomial spline in off-step points to rise the order of accuracy. Based...