Some comparisons of difference schemes on meshes of Shishkin and Bakhvalov type.
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...
Some constructive applications of -representations to integration of PDEs
Two new applications of -representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane . 2. Employing -representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.
Some convergence acceleration processes for a class of vector sequences
Let be some vector sequence, converging to S, satisfying , where are constant vectors independent of n. The purpose of this paper is to provide acceleration methods for these vector sequences. Comparisons are made with some known algorithms. Numerical examples are also given.
Some Convergence Results for Asynchronous Algorithms.
Some Convergent Jacobi-like Procedures for Diagonalising J-Symmetric Matrices.
Some Current Questions on Solving Linear Elliptic Problems.
Some differential equations with delay
Some double integral inequalities and applications.
Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*
Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini's conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam...
Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*
Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini's conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam...
Some equilibrium and mixed models in the finite element method
Some Equilibrium Finite Element Methods for Two- Dimensional Elasticity Problems.
Some facts related to the papers by L. V. Kantorovich reproduced in this issue.
Some fast finite-difference solvers for Dirichlet problems on general domains
The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.
Some fast finite-difference solvers for Dirichlet problems on special domains
The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some features of the nodal recovery of gradients from finite element approximations which produces superconvergence
Some fourth-order formulae of a certain method of Zurmühl
Some functions of eigenvalues of normal operator
Kellogg's iterations in the eigenvalue problem are discussed with respect to the boundary spectrum of a linear normal operator.