We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes. 1. Introduction. In this paper, we characterize the convergence in distribution to a normal N (0, 1) law f...

A new parametric family of iterative schemes for solving nonlinear systems is presented. Fourth-order convergence demonstrated and its stability analyzed as a function the parameter values. This study allows us to detect most stable elements class, find fractals in boundary basins attraction reject those with chaotic behavior. Some numerical tests show performance methods, confirm theoretical r...

Two discretizations of a 9-velocity Boltzmann equation with a BGK collision operator are studied. A Chapman-Enskog expansion of the PDE system predicts that the macroscopic behavior corresponds to the incompressible Navier-Stokes equations with additional terms of order Mach number squared. We introduce a fourth-order scheme and compare results with those of the commonly used lattice Boltzmann ...

A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss–Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test the accuracy of t...

In this paper, a highly accurate parallel difference scheme for the fourth-order diffusion equation is studied. Based on a group of new Saul’yev type asymmetric difference schemes, a high-order, unconditionally stable and parallel alternating group explicit scheme is derived. The scheme is fourth-order truncation error in space, which is much more accurate than the known methods. Numerical expe...

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbat...

In this paper, we propose a new cubically convergent family of superHalley method based on power means. Some well-known methods can be regarded as particular cases of the proposed family. New classes of higher (third and fourth) order multipoint iterative methods free from second order derivative are derived by semi-discrete modifications of above-mentioned methods. It is shown that super-Halle...