A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous q...

Basis functions of biquadratic polynomial spline spaces over hierarchical T-meshes are constructed. The basis functions are all tensor-product B-splines, which are linearly independent, nonnegative and complete. To make basis functions more efficient for geometric modeling, we also give out a new basis with the property of unit partition. Two preliminary applications are given to demonstrate th...

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary differential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate. Received: 2 February 2014, Revised: 4 May 201...

This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key strategy is linear space embedding with the operator of mixed partial derivative. The dimension of the original space equals the difference between the dimension o...

In this paper, we have obtained existence, uniqueness, best error bound and convergence properties of C Deficient Quartic Spline Interpolation. Classification Code Ø 41A05, 65D07.

Quartic B-spline time integration method has been recently proposed for solving linear problems in structural dynamics. This paper developed this method to nonlinear dynamic analysis of single-degree-of-freedom (SDOF) systems under exploding loads. Using quartic B-spline basis function, this method gained second order of acceleration at each time-step. Thus it benefits from high accuracy compar...

Abstract Via modified quartic hyperbolic B-spline DQM, Burgers’ equation is numerically approximated in the current study. Ten numerical instances are discussed, and findings compared with those already existence exact results. Error norms assessed, shown tabular as well graphical formats, to validate resilience applicability portion of established system. Matrix stability analysis approach use...

Estimates of risk-neutral densities future asset returns have been commonly used for pricing new financial derivatives, detecting profitable opportunities, and measuring central bank policy impacts. We develop a nonparametric approach estimating the density prices reformulate its estimation into double-constrained optimization problem. evaluate our using S&P 500 market option from 1996 ...