On the Spectrum Structure for One Difference Eigenvalue Problem With Nonlocal Boundary Conditions

Abstract

The difference eigenvalue problem approximating the one-dimensional differential equation with the variable weight coefficients in an integral conditions is considered. The cases without negative eigenvalue in the spectrum of difference eigenvalue problem were analyzed. Analysis of the conditions of stability of difference schemes for parabolic equations was carried out according to the theoretical results and results of the numerical experiment.

Investigation of a Discrete Sturm–liouville Problem With Two-Point Nonlocal Boundary Condition and Natural Approximation of a Derivative in Boundary Condition

“…In the case of NBCs, properties of discrete SLP (dSLP) were investigated in [1,2,5,6,13,15,22] and results were used for theoretical justification of stability Finite Difference Schemes (FDS) for various elliptic, hyperbolic and parabolic equations [20,21]. Finite difference method together with asymtotic formulas for eigenvalues [26,27] gives very good approximation of spectrum for differential SLP.…”