Stability of Solutions of Differential-operator and Operator-difference Equations in the Sense of Perturbation of Operators

2006 ◽  
Vol 6 (3) ◽  
pp. 269-290 ◽  
Author(s):  
B. S. Jovanović ◽  
S. V. Lemeshevsky ◽  
P. P. Matus ◽  
P. N. Vabishchevich
Keyword(s):  
Differential Operator ◽  
Difference Equations ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Order Differential Operator ◽  
Stability Of Solutions ◽  
Operator Equations ◽  
The Difference ◽  
Coefficient Stability

Abstract 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 the coefficient stability for onedimensional parabolic and hyperbolic equations as well as for the difference schemes approximating the corresponding differential problems.

scholarly journals COEFFICIENT STABILITY OF OPERATOR‐DIFFERENCE SCHEMES WITH TIME VARIABLE OPERATORS

1998 ◽  
Vol 3 (1) ◽  
pp. 152-159
Author(s):  
I. N. Panayotova
Keyword(s):  
Differential Operator ◽  
Initial Data ◽  
A Priori ◽  
Time Variable ◽  
Energy Space ◽  
Difference Schemes ◽  
Operator Equations ◽  
Variable Operator ◽  
The Right ◽  
Coefficient Stability

The problem of the coefficient stability for operator‐ difference schemes with variable operator is investigated. A priori coordinated estimates in the L 2‐norm are obtained for differential‐operator equations and operator‐difference schemes. Estimates in the energy space HA for coefficient stability and stability with respect to the right-hand side and the initial data are proved under more strong assumptions for operator's perturbation.

scholarly journals Compact Difference Schemes on a Three-Point Stencil for Second-Order Hyperbolic Equations

2021 ◽  
Vol 57 (7) ◽  
pp. 934-946
Author(s):  
P. P. Matus ◽  
Hoang Thi Kieu Anh
Keyword(s):  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
Initial Conditions ◽  
Second Order ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
The Difference ◽  
Difference Solution

Abstract We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable coefficients. New compact schemes are proposed for one type of second-order quasilinear hyperbolic equations. In the case of constant coefficients, we prove the strong stability of the difference solution under small perturbations of the initial conditions, the right-hand side, and the coefficients of the equation. A priori estimates are obtained for the stability and convergence of the difference solution in strong mesh norms.

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