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 bound...

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the newmethod are given and the efficiency of the newmethod is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-or...

For planar spline curves and bivariate box-spline functions, the cone of normals of a polynomial spline piece is enclosed by the cone of normals of its spline control polyhedron. This note collects some concrete examples to show that this is not true for subdivision surfaces, both at extraordinary points and in the regular, box-spline setting. A larger set, the cross products of families of con...

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...

a class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is 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. convergence anal...

This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a diffe...

A complex geometric shape is often a composition of a set of simple ones, which may differ from each other in terms of their mathematical representations and the ways in which they are constructed. One of the necessary requirements in combining these simple shapes is that their original shapes can be preserved as much as possible. In this paper, a set of partial shape-preserving (PSP) spline ba...

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...