The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The principle is a singular modification of the mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. The major interest of these methods is ...

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equati...

Due to the principle of regularization by restricting the number of degrees of freedom, truncating the Cholesky factorization of a symmetric positive definite matrix can be expected to have a stabilizing effect. Based on this idea, we consider four different approaches for regularizing ill-posed linear operator equations. Convergence in the noise free case as well as — with an appropriate a pri...

This paper is concerned with the solution of large-scale linear discrete ill-posed problems. The determination of a meaningful approximate solution of these problems requires regularization. We discuss regularization by the Tikhonov method and by truncated iteration. The choice of regularization matrix in Tikhonov regularization may significantly affect the quality of the computed approximate s...

In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The ...

fuzzy liner systems of equations, play a major role in several applications in various area such as engineering, physics and economics. in this paper, we investigate the existence of a minimal solution of inconsistent fuzzy matrix equation. also some numerical examples are considered.

this paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp m-matrix. thefuzzy linear system (fls) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. however, solving this crisp system isdifficult for large n because of dimensionality problems . it is shown that thisdifficulty may be avoide...

Vertical averaging of the three dimensional incompressible Euler equations leads to several reduced dimension models of ow over topography, including the one-layer and two-layer classic shallow water equations, and the one-layer and two-layer nonhydrostatic Green-Naghdi equations. These equations are derived and their well-posedness is discussed. Several implicit and explicit nite diierence app...

This paper studies the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator L that can be defined through both an integral kernel and a Fourier multiplier. When the symbol of L is represented by |ξ| a(|ξ|) with a satisfying lim|ξ|→∞ a(|ξ|) |ξ|σ = 0 for any σ > 0, we obtain the global well-posedness. A special cons...

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.