In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equation with a smooth kernel. Using a sufficiently accurate numerical quadrature rule, we obtain super-convergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and 𝐿2-norm. Numerical examples are given to illustrate the theoretical results.

Sorting or ordering is an arrangement of a set of items of a list in a certain order. Several sorting algorithms and methods are available. In this paper, we focus on the simplest but not highly efficient bubble sort algorithm. Rearranging parallel computing, i.e., message passing interface (MPI), it is explained why parallel architectures are now mainstream. Recently, parallel computing has become one of the most important aspects of computer science and it has showed dominance especially in the field of analyzing high-performance problems. One of the major results is the type of data structure obtained by using 3D array of char, which shows faster result, instead of using a vector of string with extra overhead. The threads (slaves) sort part of the list and return to the master thread, which merges all small lists in one final sorted list. This study shows an increase in speed and efficiency with the increase in number of threads, indicating an increase in the efficiency of bubble sort algorithm.

Suppose that T is a tree. AbuHijleh has shown that T² is a divisor graph iff T is a caterpillar with diam(T) ≤ 5. In this paper we characterize when T³ and T⁴ are divisor graphs.