Stability of Solutions of Second-Order Differential-Operator Equations and of Their Difference Approximations

2020 ◽  
Vol 56 (7) ◽  
pp. 923-934
Author(s):  
S. V. Lemeshevsky ◽  
P. P. Matus
Keyword(s):  
Differential Operator ◽  
Second Order ◽  
Order Differential Operator ◽  
Stability Of Solutions ◽  
Operator Equations ◽  
Difference Approximations

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.

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