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 current research develops derivative-free family with memory methods with 100% improvement in the order of convergence. They have three parameters. The parameters are approximated and increase the convergence order from 4 to 6, 7, 7.5 and 8, respectively. Additionally, the new self-accelerating parameters are constructed by a new way. They have the properties of simple structures and they a...

The main effort of our light-front community has been in the past ten years to develop new techniques for solving QCD, be it DLCQor renormalisationgroupbased methods (for review see [1]). In practice the usefulness of any procedure (which includes the question of convergence) is often determined by how well its first approximation captures the essential features of the system under consideratio...

We study the convergence rate of an asymptotic expansion for the elliptic and parabolic operators with rapidly oscillating coefficients. First we propose homogenized expansions which are convolution forms of Green function and given force term of elliptic equation. Then, using local Lp-theory, the growth rate of the perturbation of Green function is found. From the representation of elliptic so...

The nonuniform convergence of the Fourier series for discontinuous functions, and in particular the oscillatory behavior of the finite sum, was already analyzed by Wilbraham in 1848. This was later named the Gibbs phenomenon. This article is a review of the Gibbs phenomenon from a different perspective. The Gibbs phenomenon, as we view it, deals with the issue of recovering point values of a fu...