We construct and analyze the backward Euler method for one nonlinear one-dimensional parabolic equation with nonlocal boundary condition. The main objective of this article is to investigate stability convergence difference scheme in maximum norm. For purpose, we use M-matrices theory. describe some new approach estimation error solution majorant it. Some conclusions discussion our are presented.

The paper is devoted to the study of mappings satisfying inverse Poletsky inequality. We local behavior these mappings. are most interested in case when corresponding majorant integrable on some set spheres positive linear measure. Our main result a logarithmic Hölder continuity such at inner points. As corollary, we have established existence continuous ACL-solution Beltrami equation, which co...

In this article we develop a max-strategy improvement algorithm for computing least fixpoints of operators on R (with R := R ∪ {±∞}) that are point-wise maxima of finitely many monotone and order-concave operators. Computing the uniquely determined least fixpoint of such operators is a problem that occurs frequently in the context of numerical program/systems verification/analysis. As an exampl...

In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.

Using inequalities for a certain function appearing in the half-linear version of Picone’s identity, we show that oscillatory properties of the half-linear second-order differential equation (r(t)Φ(x′))′ + c(t)Φ(x) = 0, Φ(x) = |x|p−2x, p > 1, can be investigated via oscillatory properties of a certain associated second-order linear differential equation. This linear equation plays the role of a...

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α (0 < α < 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of mod...

Recently a new class of schemes, called Time Relaxed Monte Carlo (TRMC) has been introduced for the numerical solution of the Boltzmann equation of gas dynamics. The motivation is to propose a systematic framework to derive Monte Carlo methods effective near the fluid dynamic regime. Before the methods can be accepted as alternative tools to other methods, they have to show that they are able t...

This paper studies the positioning problem based on two-way time-of-arrival (TW-TOA) measurements in asynchronous wireless sensor networks. Since the optimal estimator for this problem involves difficult nonconvex optimization, we propose two suboptimal estimators based on squared-range least squares and least absolute mean of residual errors. The former approach is formulated as a general trus...

The task of obtaining the exact values best approxima-tions by trigonometric polynomials continuous or summable functions originates from works P. L. Chebyshev, who, back in 1950s, posed problem finding polynomial, that de-viates least a given function. Subsequently this direction theory approximation got further development thanks to K. Weierstrass, D. Jackson, S. N. Bernstein, Valle-Poussin a...