# On the Stability of Differential-operator Equations and Operator-difference Schemes as t â†’ âˆž

## Related Articles

- STABILITY OF SOLUTIONS OF DIFFERENTIAL-OPERATOR AND OPERATOR-DIFFERENCE EQUATIONS IN THE SENSE OF PERTURBATION OF OPERATORS. Jovanović, B. S.; Lemeshevsky, S. V.; Matus, P. P.; Vabishchevich, P. N. // Computational Methods in Applied Mathematics;2006, Vol. 6 Issue 3, p269
Estimates of stability in the sense perturbation of the operator for solving first- and second-order differential-operator equations have been obtained. For two- and three-level operator-difference schemes with weights similar estimates hold. Using the results obtained, we construct estimates of...

- ASYMPTOTIC STABILITY OF A THREE-LEVEL OPERATOR-DIFFERENCE SCHEME. Jovanović, B. S. // Computational Methods in Applied Mathematics;2006, Vol. 6 Issue 4, p405
Asymptotic stability of linear three-level operator-difference schemes is investigated in the case of commutative operators. Some new a priori estimates are obtained.

- On the stability of an operator-difference scheme of the type of hyperbolic-parabolic systems of differential equations. Zhelezovskii, S. // Differential Equations;Aug2011, Vol. 47 Issue 8, p1139
We obtain results on the stability of a three-layer operator-difference scheme that generalizes a class of difference and projection-difference schemes for linear coupled thermoelasticity problems.

- A Criterion for Coefficient Stability. Lemeshevskii, S. V.; Matus, P. P.; Naumovich, A. R. // Differential Equations;Jul2004, Vol. 40 Issue 7, p1043
Analyzes the stability of the solution of the differential problem under perturbations of the initial conditions, the right-hand side, and the operator coefficients. Definition of strong stability of a two-level operator-difference scheme; Notions of stability of a scheme with respect to the...

- SM-stability of operator-difference schemes. Vabishchevich, P. // Computational Mathematics & Mathematical Physics;Jun2012, Vol. 52 Issue 6, p887
The spectral mimetic (SM) properties of operator-difference schemes for solving the Cauchy problem for first-order evolutionary equations concern the time evolution of individual harmonics of the solution. Keeping track of the spectral characteristics makes it possible to select more appropriate...

- An Operator-Difference Method for Telegraph Equations Arising in Transmission Lines. Koksal, Mehmet Emir // Discrete Dynamics in Nature & Society;2011, Special section p1
A second-order linear hyperbolic equation with time-derivative term subject to appropriate initial and Dirichlet boundary conditions is considered. Second-order unconditionally absolutely stable difference scheme in (Ashyralyev et al. 2011) generated by integer powers of space operator is...

- On the Strong Stability of First-Order Operator-Differential Equations. Bojovic, D. R.; Jovanovic, B. S.; Matus, P. P. // Differential Equations;May2004, Vol. 40 Issue 5, p703
The notion of stability of a solution of a differential equation is well known. Strong (or coefficient) stability is the stability of the solution under perturbations of the coefficients of the equation. On the abstract level, a perturbation of the coefficients can be treated as a perturbation...

- Operator-difference schemes for a class of systems of evolution equations. Vabishchevich, P. // Mathematical Notes;Jan2013, Vol. 93 Issue 1/2, p36
For a special system of evolution equations of first order, discrete time approximations for the approximate solution of the Cauchy problem are considered. Such problems arise after the spatial approximation in the SchrÃ¶dinger equation and the subsequent separation of the imaginary and real...

- Three-level schemes of the alternating triangular method. Vabishchevich, P. // Computational Mathematics & Mathematical Physics;Jun2014, Vol. 54 Issue 6, p953
In this paper, the schemes of the alternating triangular method are set out in the class of splitting methods used for the approximate solution of Cauchy problems for evolutionary problems. These schemes are based on splitting the problem operator into two operators that are conjugate transposes...

- EXPLICIT-IMPLICIT SPLITTING SCHEMES FOR SOME SYSTEMS OF EVOLUTIONARY EQUATIONS. GASPAR, FRANCISCO; GRIGORIEV, ALEXANDER; VABISHCHEVICH, PETR // International Journal of Numerical Analysis & Modeling;2014, Vol. 11 Issue 2, p346
In many applied problems, the individual components of the unknown vector are interconnected and therefore splitting schemes are applied in order to get a simple problem for evaluating unknowns at a new time level. On the basis of additive schemes (splitting schemes), there are constructed...