On The Stability Of Finite-Difference Schemes For Parabolic Equations Subject To Integral Conditions With Applications To Thermoelasticity

Abstract

-The stability of implicit difference scheme for parabolic equations subject to integral conditions, which correspond to the quasi-static flexure of a thermoelastic rod is considered. The stability analysis is based on the spectral structure of matrix of the difference scheme. The stability conditions obtained here differ from those presented in the articles of other authors.2000 Mathematics Subject Classification: 65M06, 65M12.

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

“…Λ x is a nonsymmetric matrix (it becomes symmetric iff γ 0 = γ 1 = 0, namely, if there are no nonlocal conditions). Its eigenvalues are given in [30].…”

On Construction and Analysis of Finite Difference Schemes for Pseudoparabolic Problems With Nonlocal Boundary Conditions

“…Let us consider the case of operators A = −L, B = −ηL. Then it is proved in [24] that for γ 1 + γ 2 < 2 all eigenvalues of the operator A are real and positive. Then the stability of the finite difference scheme (3.1), (3.2) can be investigated by using the matrix diagonalization method (1.6).…”

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…The analysis of stationary problem with one classical boundary condition (γ 0 = 0) and another NBC [197,214,218] and investigation of auxiliary stationary problems [107,187,198] shows that restrictions γ 0 0 and γ 1 0 are not necessary, and, in general case, we can take γ 0 , γ 1 ∈ R. The main research tools in [35,36] were the maximum principle and comparison theorems. Existence and uniqueness of a solution for the stationary problem is equivalent to existence of zero eigenvalue.…”

“…FD method (functional-discrete method) is derived and analysed for calculating of eigenvalues, particularly complex eigenvalues. Jesevičiūtė and Sapagovas [107] investigated the stability of FDS for parabolic equation with integral type NBCs with variable weight functions…”