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Nonlocal boundary value problem with Poisson’s operator is studied. Existence, uniqueness and a priori estimate are established for classical solution. Second-order of accuracy for difference approximation is reached in difference metrics C,W2² . [ABSTRACT FROM AUTHOR]

In the present paper, we investigate a nonlocal boundary problem for the Laplace equation in a half-disk, with opposite flows at the part of the boundary. The difference of this problem is the impossibility of direct applying of the Fourier method (separation of variables). Because the corresponding spectral problem for the ordinary differential equation has the system of eigenfunctions not forming a basis. A special system of functions based on these eigenfunctions is constructed. This system has already formed the basis. This new basis is used for solving the nonlocal boundary value problem. The existence and the uniqueness of the classical solution of the problem are proved. [ABSTRACT FROM AUTHOR]

In this work, the nonlocal boundary value problem for a telegraph equation in a Hilbert space is conceived. Stability estimates for the solution of this problem are obtained. The first and second order of accuracy difference schemes for the approximate solution of this problem are constructed. Stability estimates for the solution of these difference schemes are established. In implementations, two mixed problems for telegraph partial differential equations are investigated. The methods are showed by numerical experiments. [ABSTRACT FROM AUTHOR]

The nonlocal boundary value problem for elliptic-Schrödinger equations is considered. The stability estimates for the solution of this problem are presented. In applications, the stability estimates of the mixed type boundary value problems for elliptic-Schrödinger equations are obtained. [ABSTRACT FROM AUTHOR]

This work investigates the approximate solution for fourth-order multi-point boundary value problem represented by linear integro-differential equation involving nonlocal integral boundary conditions by using the reproducing kernel method (RKM). The investigated solution is represented in the form of a series with easily computable components in the reproducing kernel space. When the used algorithm for approximation is applied directly for the given original conditions, it can be very troublesome to compute the reproducing kernel of space. Therefore firstly, it is considered more appropriate conditions to be computed the kernel easily than original ones. Nextly, the original conditions are taken into account. Analysis is illustrated by a numerical example. The results demonstrate that the method is quite accurate and effective. [ABSTRACT FROM AUTHOR]

The Bitsadze-Samarskii type nonlocal boundary value problem ... for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The fourth order of accuracy difference scheme for approximate solution of the problem is presented. The well posedness of this difference scheme in difference analogue of Holder spaces is established. [ABSTRACT FROM AUTHOR]