In this paper an efficient numerical scheme to approximate the solutions of fifth-order boundary value problems in a finite domain with two different types of boundary conditions has been prsented, by taking basis functions with quartic Bsplines and weight functions with quintic B-splines in PetrovGalerkin method. In this method, the quartic B-splines and quintic B-splines are redefined into ne...

Collocation method using quintic B-splines finite element have been developed for solving numerically the HirotaSatsuma coupled MKdV equation. Accuracy of the proposed method is shown numerically by calculating conservation laws, 2 L and  L norms on studying of a soliton solution. It is shown that the collocation scheme for solutions of the MKdV equation gives rise to smaller errors and is qui...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...

In order to construct a C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme [5]. In this paper we introduce a nodal macroelement on the 12-split...

To address the issues of low efficiency and lengthy running time associated with trajectory planning for 6-degree-of-freedom manipulators, this paper introduces a novel solution that generates time-optimal path manipulator while adhering to its kinematic limitations. The proposed method comprises several stages. Firstly, kinematics are analyzed. Secondly, manipulator’s joint-space points interp...