Том 27, № 2 (2016)

We derive integral relationships for electromagnetic fields, integral recalculation formulas for anomalous electric and magnetic fields, and integral boundary conditions. The efficiency of the finite-difference–integral method is checked by computing the apparent resistance curves for the graben model. Apparent resistance curves computed from finite-difference formulas and from formulas with integral smoothing are compared. Finite-difference graphs are polygonal curves that for small wavelengths lie below the smoothed curves, because the finite-difference computation of the derivative as if reduces the impact of the surface skin effect on the apparent resistance. As the wavelength increases, the surface skin effect diminishes and the finite-difference curves approach the integral curves.

We consider the problem of localizing the region of the heart damaged by myocardial infarct. For the two-dimensional modified FitzHugh–Nagumo mathematical model, this inverse problem involves determining the coefficient dependent on spatial variables for a system of partial differential equations in a region with a localized source of cardiac excitation. Additional dynamical measurements of the potential are carried out on the inner boundary of the region representing the section of the heart and its ventricles by a horizontal plane. Potential measurements on the inner boundary correspond to data obtained from ventricular catheters. A numerical method is proposed for the solution of this inverse problem and results of computer experiments are reported.

The numerical method we have previously developed to search for soliton solutions is applied in this article to find spatial solitons described by a nonlinear Schroedinger equation. We show in detail how to derive the Schroedinger equation from Maxwell’s equations and now to construct a one-soliton analytical solution for the one-dimensional Schroedinger equation. The proposed numerical method is appropriate to search for spatial solitons, which is corroborate by comparing the numerical results with the analytical solution.

In this study, the Rudin, Osher, and Fatemi (ROF) model is considered to restore images. To this end, the compact finite difference (CFD) method is introduced to approximate the spatial derivatives in the ROF model. Moreover, two filters are presented to improve the performance of the first- and second-order derivative approximation. The third-order total variation diminishing Runge-Kutta (TVD-RK3) method is applied to solve the obtained system along the time axis. Two examples are given to show the efficiency and accuracy of the method.

In this article, we prove the existence and convergence theorems of the solution for a system of hierarchical variational inequality problem in Hilbert spaces. In this paper, we use Maingé’s approach for finding a solution of the system of hierarchical variational inequality problems. Our result in this article improves, extends, and generalizes some well-known corresponding results in the literature.

The article considers a three-point central-difference scheme for the transfer equation, with different kinds of special boundary conditions that reduce wave reflection from artificial boundaries. For the corresponding problems, we prove stability in grid energy norms analogous to the ordinary L₂-norm or the differential (Sobolev) norm.

Analysis of long time series is relevant in many current applications. These investigations are usually carried out on multiprocessor computers (supercomputers). However, supercomputer calculations are efficient only if the time-series processing algorithms are sufficiently parallelized. In this article, we propose a parallel algorithm that detects shift points of the time-series mean — a highly important task in many applications. The algorithm breaks the time series into segments and looks for shift points on each segment using a statistical test. The critical values have been calculated for this test. An additional test reduces the number of false detections.