On the spectral stability in subspaces for difference schemes with nonlocal boundary conditions

2013 ◽  
Vol 49 (7) ◽  
pp. 815-823 ◽  
Author(s):  
A. V. Gulin
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Spectral Stability ◽  
Difference Schemes

Difference Schemes with Nonlocal Boundary Conditions

2001 ◽  
Vol 1 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Alexei V. Goolin ◽  
Nikolai I. Ionkin ◽  
Valentina A. Morozova
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Equation ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Conduction Equation ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient

AbstractThe paper deals with the stability, with respect to initial data, of difference schemes that approximate the heat-conduction equation with constant coefficients and nonlocal boundary conditions. Some difference schemes are considered for the one-dimensional heat-conduction equation, the energy norm is constructed, and the necessary and sufficient stability conditions in this norm are established for explicit and weighted difference schemes.

scholarly journals ON CONSTRUCTION AND ANALYSIS OF FINITE DIFFERENCE SCHEMES FOR PSEUDOPARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2014 ◽  
Vol 19 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Raimondas Čiegis ◽  
Natalija Tumanova
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
The Stability

In this paper the one- and two-dimensional pseudoparabolic equations with nonlocal boundary conditions are approximated by the Euler finite difference scheme. In the case of classical boundary conditions the stability of all schemes is investigated by the spectral method. Stability regions of finite difference schemes approximating pseudoparabolic problem are compared with the stability regions of the classical discrete parabolic problem. These results are generalized for problems with nonlocal boundary conditions if a matrix of the finite difference scheme can be diagonalized. For the two-dimensional problem an efficient algorithm is constructed, which is based on the combination of the FFT method and the factorization algorithm. General stability results, known for the three level finite difference schemes, are applied to investigate the stability of some explicit approximations of the two-dimensional pseudoparabolic problem with classical boundary conditions. A connection between the energy method stability conditions and the spectrum Hurwitz stability criterion is shown. The obtained results can be applied for pseudoparabolic problems with nonlocal boundary conditions, if a matrix of the finite difference scheme can be diagonalized.

scholarly journals STATIONARY PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2001 ◽  
Vol 6 (2) ◽  
pp. 178-191 ◽  
Author(s):  
R. Čiegis ◽  
A. Štikonas ◽  
O. Štikoniene ◽  
O. Suboč
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Maximum Norm ◽  
Finite Difference Schemes ◽  
Stability Estimates ◽  
Stationary Problems ◽  
Theoretical Results

In this article a stationary problems with general nonlocal boundary conditions is considered. The differential problems and finite difference schemes for solving this problem are investigated. Stability estimates are proved in the maximum norm and the non‐negativity of the solution is investigated. All theoretical results are illustrated by representative examples.

Stability Criterion of Difference Schemes for the Heat Conduction Equation with Nonlocal Boundary Conditions

2006 ◽  
Vol 6 (1) ◽  
pp. 31-55 ◽  
Author(s):  
A. Gulin ◽  
N. Ionkin ◽  
V. Morozova
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Stability Theory ◽  
Heat Conduction Equation ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Energy Norm ◽  
Conduction Equation ◽  
L2 Norm

Abstract The elements of the stability theory of nonselfadoint difference schemes for nonstationary problems of mathematical physics are discussed. Difference schemes for the heat conduction equation with nonlocal boundary conditions are considered in detail from the viewpoint of the general stability theory of two-layer operator-difference schemes. The necessary and sufficient stability conditions in the sense of the initial data in special energy norm have been found. The equivalence of the energy norm to the grid L2-norm has been proved. A priori estimates expressing the difference schemes stability in the sense of the right-hand side have been constructed.

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