In this paper, Quintic spline in o -step points is used for the solution of fourth-order boundary value problems. Spline relations and boundary formulas are developed and the convergence analysis of the given method is investigated. Numerical illustrations are given to show the applicability and e ciency of our method.

Most shapes are simply too complicated to define using a single Bézier curve. A spline curve is a sequence of curve segments that are connected together to form a single continuous curve. For example, a piecewise collection of Bézier curves, connected end to end, can be called a spline curve. Overhauser curves are another example of splines. The word “spline” can also be used as a verb, as in “...

The problem of interpolation of discrete set of data on the interval [a, b] representing the function f is investigated. A family of C splines with one free generating function is introduced in order to solve this problem. Cubic C splines belong to this family. The required conditions which must satisfy the generating function in order to obtain explicit interpolants are presented and examples ...

Data coding have emerged in different directions. Various real time applications focused towards the improvement of data codings for efficient and accurate usage of available resources. In such application where resources are constrained, data coding systems are facing the limitation of processing speed and accuracy. Applications where speed of computation for

To de ne spline subdivision schemes for general compact sets we use the representation of spline subdivision schemes in terms of repeated averages and replace the usual average convex combination by a binary averaging operation between two compact sets introduced in and termed here the metric average These schemes are shown to converge in the Hausdor metric and to provide O h approximation x In...

We prove that a compactly supported spline function of degree k satisses the scaling equation (x) = P N n=0 c(n)(mx?n) for some integer m 2, if and only if (x) = P n p(n)B k (x?n) where p(n) are the coeecients of a polynomial P(z) such that the roots of P(z)(z ? 1) k+1 are mapped into themselves by the mapping z ! z m , and B k is the uniform B-spline of degree k. Furthermore, the shifts of for...

We propose the evolution of curves in direction of their unit normal using a combined implicit and explicit spline representation according to a given velocity field. In the implicit case we evolve a level set function for segmentation and geometry reconstruction in 2D images. The level set approach allows for topological changes of the evolving curves. The evolution of the explicit B-spline cu...

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree...

A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. Refinable splines have been studied in several papers, most noticably in [7] for integer dilations and [3] for real dilations. There are general characterizations in these papers, but these characte...

Singularly perturbed boundary value problem can be solved using various techniques. The solution of the following fourth order self adjoint singularly perturbed boundary value problem is approximated using quintic spline Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(1)(a) = α2, y(1)(b) = α3, } or Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(2)(a) = α4, y...