Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69773120130101On convergence of He’s variational iteration method for nonlinear partial differential equations172441310.22067/ijnao.v3i1.18810ENJafar Saberi -NadjafiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Asghar GhorbaniDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article19700101This 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69773120130101Block-Coppels chaos in set-valued discrete systems9122441410.22067/ijnao.v3i1.18812ENBahman HonaryFaculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Mojtaba JazaeriFaculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article19700101Let (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) =<br />{f (a) : a ∈ A} . We show that Block-Coppels chaos in f implies Block-Coppels chaos in ¯f if f is a bijection.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69773120130101A level set moving mesh method in static form for one dimensional PDEs13302441510.22067/ijnao.v3i1.18813ENMaryam Arab AmeriDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.0000-0003-0269-4547Journal Article19700101In 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69773120130101Accelerated normal and skew-Hermitian splitting methods for positive definite linear systems31442441610.22067/ijnao.v3i1.18830ENF. ToutounianDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.0000-0003-4805-7850D. HezariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article19700101For 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69773120130101An alternative 2-phase method for evaluating of DMUs using DEA45542441710.22067/ijnao.v3i1.18824ENMohammadreza AlirezaeeSchool of Mathematics, Iran University of Sciences and Technology, Tehran, Iran.Journal Article19700101Computationally, 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.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69773120130101Finite volume method for one dimensional biot poroelasticity system in multilayered domains55722441810.22067/ijnao.v3i1.18827ENM. NamjooDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.H. Atighi LorestaniDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article19700101R. 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.