in this paper , the quintic b-spline collocation scheme is employed to approximate numerical solution of the kdv-like rosenau equation . this scheme is based on the crank-nicolson formulation for time integration and quintic b-spline functions for space integration . the unconditional stability of the present method is proved using von- neumann approach . since we do not know the exact solution...

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

We construct a suitable B-spline representation for a family of bivariate spline functions with smoothness r ≥ 1 and polynomial degree 3r − 1. They are defined on a triangulation with PowellSabin refinement. The basis functions have a local support, they are nonnegative and they form a partition of unity. The construction involves the determination of triangles that must contain a specific set ...

This paper focuses on self-similar gravitational collapse solutions of the Einstein--axion-dilaton configuration for two conjugacy classes SL(2, R) transformations. These are invariant under spacetime dilation, combined with internal For first time in literature, we apply nonlinear statistical spline regression methods to estimate critical spherical black hole four dimension. include truncated ...

Mathematical concepts of multivariate parametric solids, their description by a B-spline basis functions are discussed. Parametric solids can model both the shape and unisotropic interior. Three types of parametric solids i.e. Coons body 0, 1 and 2 are used to demonstrate the interior modelling often used as initial or boundary conditions in numerical simulation. Multiple parametric solids elem...

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. The spline kernels are useful for continuous signal processing algorithms that involve Bspline inner-products or the convolution of several spline basis functions. We apply our results to the derivation of spline-based algorithms for two classes of p...

We prove that the dimension of bivariate tensor–product spline spaces of bi– degree (d, d) with maximum order of smoothness on a multi–cell domain (more precisely, on a set of cells from a tensor–product grid) is equal to the number of tensor–product B–spline basis functions, defined by only single knots in both directions, acting on the considered domain. A certain reasonable assumption on the...

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...

This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit quaternion curves which share many important ...

The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion formula is applied to derive a generalized two–scale relation for B-splines with multiple knots. Furthermore, the structure of the corresponding autocorrelation symbol is investigated. In particular, it can be observed that the solvability of the cardinal Hermite spli...