Abstract—The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating functi...

The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline ...

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation functi...

We have obtained the exact-order estimates for some approximative characteristics of Sobolev classes $$ {\mathbbm{W}}_{p,\alpha}^r and Nikоl’skii–Besov {\mathbbm{B}}_{p,\theta}^r periodic functions one several variables in norm space B∞,1. Properties linear operators realizing orders best approximation {\mathbbm{B}}_{\infty, \theta}^r this by trigonometric polynomials generated a set harmonics ...

By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...

Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of higher dimensional (rational) curves and (hybrid) multivariate surfaces determined by coordinate functions that are exclusively given either by traditional trigonometric or hyperbolic polynomials in each of their variable...

Context. In April 2004 the first image was obtained of a planetary mass companion (now known as 2M1207 b) in orbit around a selfluminous object different from our own Sun (the young brown dwarf 2MASSW J1207334-393254, hereafter 2M1207 A). 2M1207 b probably formed via fragmentation and gravitational collapse, offering proof that such a mechanism can form bodies in the planetary mass regime. Howe...

The geometry of curves and surfaces plays a very important role in computer-aided geometric design (CAGD). goal this paper is to construct the Frenet frames trigonometric B\'ezier Euclidean $ 2 3- $space. Especially, curvatures these are investigated at beginning ending points.