A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. Numerical results are given t...

The (cubic) smoothing spline, of Schoenberg [S64] and Reinsch [R67], [R71], has become the most commonly used spline, particularly after the introduction of generalized cross validation by Craven and Wahba [CW79] for an automatic choice of the smoothing parameter. It is the purpose of this note to derive the computational details, in terms of B-splines, for the construction of the weighted smoo...

BACKGROUND Several recent studies have reported significant health effects of air pollution even at low levels of air pollutants, but in most of these studies linear non-threshold relations were assumed. AIMS To investigate the NO2 mortality dose-response association in nine cities participating in the APHEA-2 project using two different methods: the meta-smooth and the cubic spline method. ...

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by definition curves over stations, bow and stern contours plan lines. Thus, new knots are created applying an equal spaced subdivision on defined B-spline Then, these transversal space knots, longitudinal subdivided into equally too. Subsequently, knots. Finally,...

Every curve or surface can be defined by a set of parametric functions. For instance, (x,y,z) coordinates of the points of the curve can be given by:) (), (), (t Z z t Y y t X x = = = t being the parameter and X, Y, Z being polynomial functions in t. If X, Y and Z are 1 st degree polynomials, a line segment will be defined. In that case, two knowns only (i.e. two points or a point and a slope) ...

PH curves; B-spline curves; Nodal points; CNC interpolators; Variable feedrate control; Contour error. Abstract This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a ‘‘good’’ interpolant to the nodal points of the cubic B-spline curve, with the same ...

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...

The research status of industrial robot trajectory planning is discussed in detail, and the applicable occasions cubic polynomial interpolation, quintic B-spline curve, mixed interpolation other methods commonly used basic are comprehensively analyzed. At same time, various optimal for robots reviewed. advantages disadvantages compared important direction prospected.