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 paper deals with a short term forecasting non-stationary time series using wavelets and splines. Wavelets can decompose the series as the sum of two low and high frequency components. Aminghafari and Poggi (2007) proposed to predict high frequency component by wavelets and extrapolate low frequency component by local polynomial fitting. We propose to forecast non-stationary process u...

A graph $G$ is called $P_4$-free, if $G$ does not contain an induced subgraph $P_4$. The domination polynomial of a graph $G$ of order $n$ is the polynomial $D(G,x)=sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. Every root of $D(G,x)$ is called a domination root of $G$. In this paper we state and prove formula for the domination polynomial of no...

In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...

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...

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

In [6] Mora described an algorithm which, if it terminates, returns a noncommutative Gröbner basis. Here we follow that paper to prove the correctness of the algorithm as implemented by Dié Gijsbers and the author in GAP, cf. [1]. The algorithm is the core algorithm of the GAP package GBNP for computing with non-commutative polynomials. Earlier versions of this section were written with the hel...