The collocation methods based on cubic B-spline, are developed to approximate solution of the second and first kind Fredholm integral equations. First we collocate the solution by B-spline and the Newton-Cotes formula is used to approximate integral. Convergence analysis has been investigated and proved that the quadratur rule is fourth order convergent. The presented methods are tested to the problem, and the absolute error in the solution are compared with existing methods [1, 2, 7, 10] to verify the accuracy and convergent nature of proposed methods.

In this paper we present a new method to find simple or multiple roots of functions in a finite interval. In this method using bisection method we can find an interval such that this function is one to one on it, thus we can transform problem of finding roots in this interval into an ordinary differential equation with boundary conditions.By solving this equation using collocation method we can find a root for given function in the special interval. We also present convergence analysis of the new method. Finally some examples are given to show efficiency of the presented method.

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The mental association and the innovation of lingual and artistic relations on two syntagmatic and paradigmatic axis results in collocation in a literary speech. In the ordinary and formal language collocation is the necessary condition for a speech to be considered meaningful and coherent, but in literary language, there is a variety of aesthetic creativities and innovations that leads to the emergence of several collocations in the speech. So, in comparison with an ordinary language, several collocations can be found in a literary one. Of the most important and the most frequent linguistic and literary coordinates of Azerbaijani poetic style is the existence of an extensive proportion and relation in the network of words and the images, phones and concepts in each verse. This article reviews different types of collocations in Azerbaijani style.

The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.