Numerical Analysis of the Eigenvalue Problem for One-Dimensional Differential Operator with Nonlocal Integral Conditions

Abstract

In this paper the eigenvalue problem for one-dimensional differential operator with nonlocal integral conditions is investigated numerically. The special cases of general problem are analyzed and hypothesis about the dependence of the spectral structure of that problem on the coefficient of differential operator and the parameters of nonlocal conditions are formulated.

Semi-Implicit Difference Scheme for a Two-Dimensional Parabolic Equation With an Integral Boundary Condition

“…More exhaustively it is described in Section 5. The spectrum of the differential and difference operators with the variable coefficient has been investigated in [27,33,35].…”

On the eigenvalue problems for differential operators with coupled boundary conditions

“…The main aim of this paper is to investigate the dependence of the qualitative structure of the spectra of the differential problems (1)-(3) and (4)-(7) on the parameters γ 0 , γ 1 (to be precise, on the generalized parameter γ), i.e., to formulate conditions for the existence of zero, positive, negative or complex eigenvalues, and (when it is possible) to provide analytical expressions of eigenvalues. The eigenvalue problems for differential operators with nonlocal conditions can be investigated numerically [2]. We use technique and argument which are used, for example, in the papers [3,4] to investigate similar problems with other types of nonlocal conditions.…”