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...

In this paper one dimensional heat equation is solved using Galerkin B-spline Finite Element. Solution is obtained by reducing the initial boundary value problem to the set of Ordinary differential equations. Discretization of the spatial domain is made using cubic B-spline functions as basis functions. The numerical results obtained from the two test problems are compared with the analytical s...

Green functions of the biharmonic operator, in one and two dimensions, are used for minimum curvature interpolation of irregularly spaced data points. The interpolating curve (or surface) is a linear combination of Green functions centered at each data point. The amplitudes of the Green functions are found by solving a linear system of equations. In one (or two) dimensions this technique is equ...

This paper presents an alternative approach for removing striping patterns of Hyperion hyperspectral imagery. In this study, a cubic spline-based curve-fitting algorithm was used to estimate gray values of striping pixels in an image. The idea is to treat each line of a Hyperion image as a piece-wise spline curve in each spectral band. After identifying pixels affected by the striping noises, t...

This paper introduces a new set of orthogonal moment Functions-franklin Moments (FMs). The kernel functions of FMs is Franklin set, which is a class of complete orthogonal spline function set of degree 1. The implementation of FMs does not involve any numerical approximation and has a rather low computation complexity, since the basis set has the advantages of lower order. These properties make...

An innovative and flexible approach is introduced to address the challenge of self-organizing a group mobile robots into cubic-spline-based patterns without any requirement control points. Besides self-organization robots, incorporates potential field-based for obstacle/collision avoidance. This will offer more flexibility swarm efficiently deal with many practical situations, including smoothl...

Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and u...

We use C 1 quintic superspline functions to interpolate any given scattered data. The space of C 1 quintic superspline functions is introduced in Lai and LeMehaute'99] and is an improvement of the Alfeld scheme of 3D scattered data interpolation. We have implemented the spline space in MATLAB and tested for the accuracy of reproduction of all quintic polynomials. We present some numerical evide...

Stitching or merging B-spline curves is a frequently used technique in geometric modeling, and is usually implemented in CAD-systems. These algorithms are basically numerical interpolations using the least squares method. The problem, how to replace two or more curves which are generated separately and defined as B-spline curves, has well functioning numerical solutions, therefore, relatively f...