Alternating-direction method for a mildly nonlinear elliptic equation with nonlocal integral conditions

The present paper deals with a generalization of the alternating-direction implicit (ADI) method for the two-dimensional nonlinear Poisson equation in a rectangular domain with integral boundary condition in one coordinate direction. The analysis of results of computational experiments is presented

On iterative methods for some elliptic equations with nonlocal conditions

The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented. 1The research was partially supported by the Research Council of Lithuania (grant No. MIP-051/2011). 2The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014)

Investigation of Negative Critical Points of the Characteristic Function for Problems with Nonlocal Boundary Conditions

In this paper the Sturm-Liouville problem with one classical and the other nonlocal two-point or integral boundary condition is investigated. Critical points of the characteristic function are analyzed. We investigate how distribution of the critical points depends on nonlocal boundary condition parameters. In the first part of this paper we investigate the case of negative critical points

Numerical solution of nonlinear elliptic equation with nonlocal condition

Two iterative methods are considered for the system of difference equations approximating two-dimensional nonlinear elliptic equation with the nonlocal integral condition. Motivation and possible applications of the problem present in the paper coincide with the small volume problems in hydrodynamics. The differential problem considered in the article is some generalization of the boundary value problem for minimal surface equation

On the stability of explicit finite difference schemes for a pseudoparabolic equation with nonlocal conditions

A new explicit conditionally consistent finite difference scheme for one-dimensional third-order linear pseudoparabolic equation with nonlocal conditions is constructed. The stability of the finite difference scheme is investigated by analysing a nonlinear eigenvalue problem. The stability conditions are stated and stability regions are described. Some numerical experiments are presented in order to validate theoretical results

On iterative methods for some elliptic equations with nonlocal conditions

The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented

Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition

The iterative methods to solve the system of the difference equations derived from the nonlinear elliptic equation with integral condition are considered. The convergence of these methods is proved using the properties of M-matrices, in particular, the regular splitting of an M-matrix. To our knowledge, the theory of M-matrices has not ever been applied to convergence of iterative methods for system of nonlinear difference equations. The main results for the convergence of the iterative methods are obtained by considering the structure of the spectrum of the two-dimensional difference operators with integral condition. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014)

Characteristic functions for sturm—liouville problems with nonlocal boundary conditions

This paper presents some new results on a spectrum in a complex plane for the second order stationary differential equation with one Bitsadze‐Samarskii type nonlocal boundary condition. In this paper, we survey the characteristic function method for investigation of the spectrum of this problem. Some new results on characteristic functions are proved. Many results of this investigation are presented as graphs of characteristic functions. A definition of constant eigenvalues and the characteristic function is introduced for the Sturm‐Liouville problem with general nonlocal boundary conditions. First published online: 14 Oct 201

Imuninės sistemos, priklausančios nuo ŽIV ir rekombinantinio viruso sąveikos, modeliavimas

We investigate the dynamical behavior of a mathematical model of HIV and recombinant rabies virus (RV), designed to infect only the lymphocytes previously infected by HIV. This model is described by five ordinary differential equations with two discrete delays. The effect of two time delays on stability of the equilibria of the system has been studied. Stability switches and Hopf bifurcations when time delays cross through some critical values are found. Numerical simulations are performed to illustrate the theoretical results.Šiame darbe analizuojamas žmogaus imunodeficito viruso ir genetiškai modifikuoto rekombinantinio viruso sąveikos matematinis penkių diferencialinių lygčių su dviem diskrečiaisiais vėlavimais modelis. Buvo ištirta dviejų laiko vėlavimų įtaka sistemos stabilumui. Nustatytos kritinės Hopfo bifurkacijos reikšmės. Skaitiniai eksperimentai iliustruoja gautus teorinius rezultatus

Alternating direction implicit method for poisson equation with integral conditions

In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4)