In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k + kh + h) for the solution of quasi-linear parabolic equation   , , , , xx x t u f x t u u u  , 0< x <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline app...

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...

Given a triangulation 4 of a polygonal domain, we nd a reenement of 4 by choosing u t in a neighborhood of the center of the inscribed circle of each triangle t 2 4, connecting u t to the vertices of the triangle t, and connecting u t to u t 0 if t 0 2 4 shares an interior edge with t or to the midpoint v e of any boundary edge e of t. The resulting triangulation is a triangulation of Powell-Sa...

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal this study use extended cubic B-spline (ExCuBS) functions with new second order derivative approximation obtain numerical solution weakly ...

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We obtain the exact uniform approximation error on classes of functions with moduli of continuity bounded above by certain majorants. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 41A05; 41A10; 41A28

Based on the quadratic spline function, a quadratic spline collocation method is presented for the time fractional bioheat equation governing the process of heat transfer in tissues during the thermal therapy. The corresponding linear system is given. The stability and convergence are analyzed. Some numerical examples are given to demonstrate the efficiency of this method. c ©2016 All rights re...

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational Bézier patch using quartic Bézier patch. We show that our approximation method yields G (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

The paper develops a rational bi-cubic G2 (curvature continuous) analogue of the non-uniform polynomial C2 cubic B-spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly-connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic...