Iranian Journal of Numerical Analysis and Optimization
Volume:3 Issue: 1, Winter and Spring 2013

This paper deals with a novel proof of convergence of He’s variational iteration method applied to nonlinear partial differential equations by proposing a new formulation for this technique.

Computationally, selection of a proper numerical value for infinitesimal non Archimedean epsilon in DEA models has some difficulties. Although there are several algorithms for selecting the proper non-Archimedean epsilon, it is important to introduce methods in order to calculate the efficiency of DMUs without using epsilon. One of these methods is a two-phase method, which obtains the efficiency of each DMU through solving two LPs, which the second LP is depended to the first. This paper proposes a method, which is able to compute the efficiency of DMUs by two LPs, which are not depended to each other and computationally can solve in a parallel computation. The major of this method is to find two references for each unit and combine them to obtain actual reference.

Let (X, d) be a compact metric space and f: X → X be a continuous map. Consider the metric space (K(X),H) of all non empty compact subsets of X endowed with the Hausdorff metric induced by d. Let ¯ f: K(X) → K(X) be defined by ¯ f(A) = {f(a): a ∈ A}. We show that Block-Coppels chaos in f implies Block-Coppels chaos in ¯ f if f is a bijection.

In this paper, we propose an adaptive mesh approach for time dependent parial differential equations, based on a so-called moving mesh PDE(MMPDE) and level set method. It means that the velocity of mesh nodes is calculated by MMPDE and is employed as veocity in the level set equation. Then, at each time level, the mesh points are considered as the level contours of the level set function. Finally the method is merged with local time step technique.

For solving large sparse non-Hermitian positive definite linear equations, Bai et al. proposed the Hermitian and skew-Hermitian splitting methods (HSS). They recently generalized this technique to the normal and skew-Hermitian splitting methods (NSS). In this paper, we present an accelerated normal and skew-Hermitian splitting methods (ANSS) which involve two parameters for the NSS iteration. We theoretically study the convergence properties of the ANSS method. Moreover, the contraction factor of the ANSS iteration is derived. Numerical examples illustrating the effectiveness of ANSS iteration are presented.

Computationally, selection of a proper numerical value for infinitesimal non Archimedean epsilon in DEA models has some difficulties. Although there are several algorithms for selecting the proper non-Archimedean epsilon, it is important to introduce methods in order to calculate the efficiency of DMUs without using epsilon. One of these methods is a two-phase method, which obtains the efficiency of each DMU through solving two LPs, which the second LP is depended to the first. This paper proposes a method, which is able to compute the efficiency of DMUs by two LPs, which are not depended to each other and computationally can solve in a parallel computation. The major of this method is to find two references for each unit and combine them to obtain actual reference.

R. Ewing, O. Liev, R. Lazarov and A. Naumovich in [1] proposed a finite volume discretization for one dimensional Biot poroelasticity system in multilayer domains. Their discretization and exact solution are invalid. We derive valid discretization and exact solution. Finally, our numerical solution is compared with known exact solution in discrete L2 norm.