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In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate…
Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find…
We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
We consider an effective scaling approach for the free expansion of a one-dimensional quantum wave packet, consisting in a self-similar evolution to be satisfied on average, i.e. by integrating over the coordinates. A direct comparison with…
We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
We are concerned with a family of dissipative active scalar equation with velocity fields coupled via multiplier operators that can be of high-order. We consider sub-critical values for the fractional diffusion and prove global…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
Approximating solutions of ordinary and partial differential equations constitutes a significant challenge. Based on functional expressions that inherently depend on neural networks, neural forms are specifically designed to precisely…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
The main goal of this paper is to analyze a family of "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here a first step toward a rigorous…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…