A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

In [4] the first named author discussed the explicit solutions of the cubic spline interpolation problems. We are now concerned with quintic spline functions. Let 5B[0, n] denote the class of quintic spline functions S(x) defined in the interval [0, n] and having the points 0, 1, • • • , n — 1 as knots. This means that the restriction of S(x) to the interval (*>, J > + 1 ) (P = 0, • • • , n — \...

This paper presents representation techniques as the image can be represented in Cubic B-splines that are used to represent the curvilinear features of an image. The algorithm is devised to convert a raster image into vector image. The algorithm first detects the curvilinear features of the image, then based on the curvilinear edges and feature attributes it constructs a triangulation, and fina...

We introduce a modeling constructor for micro-structures and porous geometry via curve-trivariate, surface-trivariate and trivariate-trivariate function (symbolic) compositions. By using 1-, 2and 3-manifold based tiles and paving them multiple times inside the domain of a 3-manifold deforming trivariate function, smooth, precise and watertight, yet general, porous/micro-structure geometry might...

In this paper we start with Meyer-Ter-Vehn isobaric fusion model and try to reconstruct all equations by introducing a dimensionless variable ?i=ri/Rm. Then we investigate the proper sets of spark confinement parameter and temperature {Hs,Ts} which satisfy ignition conditions of spark ignition in deuterium-tritium (DT) equimolar mixture in terms of isentrope parameter, ?, implosion velocity, Ui...

Data coding have emerged in different directions. Various real time applications focused towards the improvement of data codings for efficient and accurate usage of available resources. In such application where resources are constrained, data coding systems are facing the limitation of processing speed and accuracy. Applications where speed of computation for

A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary f...