The comprehensive numerical study has been made here for the solution of One dimensional heat equation the Finite Element method is adopted for the solution with B-spline basis function the important finding of the present study is to understand the basics behind the FEM method while the B-spline basis function come into the picture here the solution is made using Quadratic B-spline and Cubic B...

In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...

We construct a suitable normalized B-spline representation for C-continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are t...

‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...

Object-based video coding requires the transmission of the object shape. This shape is sent as a binary α-plane. In lossy packetbased networks, such as the Internet, this information has a nonnegligible probability of not arriving at the receiver, and hence its loss needs to be concealed. In this paper we propose a shape concealment technique utilizing Hermite splines. The algorithm has the fol...

Receiver operating characteristics (ROC) curves have the property that they start at (0,l) and end at (1,O) and are monotonically decreasing. Furthermore, a parametric representation for the curves is more natural, since ROCs need not be single valued functions: they can start with infinite slope. In this article we show how to fit parametric splines and polynomials to ROC data with the end-poi...

We prove that the Toeplitz binary value matrix inversion associated with mth order E-spline interpolation can be implemented using only 2 (m + 1) additions. We develop pipelined architectures for real time B-spline interpolation based on simple running average filters. We also show that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can b...