This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two s...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modi ed to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using a new approach by combining cubic B-spline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Three invariants of motion are...

Abstract To obtain higher order continuous tool path, a cubic B-spline curve fitting method is presented in this paper to process the linear path. First, local polynomial with bidirectional scanning scheme proposed determine some initial dominant points. Based on these points, knot vector generated by average method, and constructed. constrain error, Newton’s based error estimation point insert...

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 ...

Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In thi...