This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the no...

In this paper we present a global-in-time non-overlapping Schwarz method applied to the one dimensional unsteady diffusion equation. We address specifically the problem with discontinuous diffusion coefficients, our approach is therefore especially designed for subdomains with heterogeneous properties. We derive efficient interface conditions by solving analytically the minmax problem associate...

We prove a partial result concerning the hard long standing problem on limit periodicity of the Jacobi matrix associated with the balanced measure on the Julia set of an expending polynomial. Besides this, connections of the problem with the Faybusovich–Gekhtman flow and many other objects (the Hilbert transform, the Schwarz derivative, the Ruelle and Laplace operators) that, we sure, they are ...

We consider methods of reduction of differential operator equations with the Fredholm operator in the main expression to regular problems. Relation between the initial conditions choice problem and the Jordan structure of operator coefficients of equations is shown. The theorem of existence and uniqueness of the initial problem is proved. The method of fundamental operators is used for construc...

We are interested in solving time dependent problems using domain decomposition method. In the classical methods, one discretizes first the time dimension and then one solves a sequence of steady problems by a domain decomposition method. In this paper, we study a Schwarz Waveform Relaxation method which treats directly the time dependent problem. We propose algorithms for the viscous Shallow W...

An overlapping domain decomposition, additive Schwarz, conjugate gradient method is presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicu-bics is applied to the Dirichlet problem for Poisson's equation on a rectangle .

We study the problem of covariant separation between first and second class constraints for the D = 10 Brink-Schwarz superparticle. Opposite to the supersymmetric light-cone frame separation, we show here that there is a Lorentz covariant way to identify the second class constraints such that, however, supersymmetry is broken. Consequences for the D = 10 superstring are briefly discussed.