In this paper, the G interpolation by Pythagorean-hodograph (PH) quintic curves in R, d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is red...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techn...

In this paper, the Khater II analytical technique is used to examine novel soliton structures for fractional nonlinear third-order Schrödinger (3-FNLS) problem. The 3-FNLS equation explains dynamical behavior of a system’s quantum aspects and ultra-short optical fiber pulses. Additionally, it determines wave function mechanical system in which atomic particles behave similarly waves. For exampl...

Tennis stroke mechanics have attracted considerable biomechanical analysis, yet current filtering practice may lead to erroneous reporting of data near the impact of racket and ball. This research had three aims: (1) to identify the best method of estimating the displacement and velocity of the racket at impact during the tennis serve, (2) to demonstrate the effect of different methods on upper...

in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. we derived the operational matrix of fractional integration of cubic and pantic b-spline scaling functions and used them to transform the mentioned equations to a ...

The fact that the Darboux frame is rotation–minimizing along lines of curvature of a smooth surface is invoked to construct rational surface patches whose boundary curves are lines of curvature. For given patch corner points and associated frames defining the surface normals and principal directions, the patch boundaries are constructed as quintic RRMF curves, i.e., spatial Pythagorean–hodograp...