In this paper, we present a survey of recent results on the Green's functions and on spectrum
for stationary problems with nonlocal boundary conditions. Results of Lithuanian …

Partial Integral Equation (PIE) representation of a Partial Differential Equation (PDE) allows
using computationally tractable algorithms for analysis, simulation, and optimal control …

In this paper, the two-level finite difference schemes for the one-dimensional heat equation
with a nonlocal initial condition are analyzed. As the main result, we obtain conditions for the …

A second-order L-stable exponential time-differencing (ETD) method is developed by
combining an ETD scheme with approximating the matrix exponentials by rational functions …

The present paper is devoted to the solution for two-dimensional hyperbolic integro-
differential equations subject to purely integral conditions. First, it is demonstrated the …

Parabolic equations with nonlocal boundary conditions have been given considerable
attention in recent years. In this paper new high-order algorithms for the linear diffusion …

Two iterative methods are considered for the system of difference equations approximating
two-dimensional nonlinear elliptic equation with the nonlocal integral condition. Motivation …

We consider the stability of the alternating direction method for wave equation with integral
boundary conditions in an energy norm. The proof of the stability is based on the properties …

Various real-world processes usually can be described by mathematical models consisted
of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest …

We use a matrix formulated algorithm to approximate solutions of a class of nonlinear
reaction-diffusion equations with nonlocal boundary conditions. Some theoretical results are …