Jovanović, B. S.; Lemeshevsky, S. V.; Matus, P. P.; Vabishchevich, P. N. Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators. (English) Zbl 1199.65306 Kragujevac J. Math. 30, 59-88 (2007). Estimates of the stability are obtained with respect to a perturbation of the operator for a solution of first- and second-order differential-operator equations. For two- and three-level operator-difference schemes with weights, similar estimates hold. Using the obtained results, estimates of coefficient stability for one-dimensional parabolic and hyperbolic equations as well as for difference schemes approximating the corresponding differential problems are constructed. Reviewer: Dejan Bojović (Kragujevac) MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations Keywords:differential-operator equation; difference schemes; stability; parabolic and hyperbolic equations PDF BibTeX XML Cite \textit{B. S. Jovanović} et al., Kragujevac J. Math. 30, 59--88 (2007; Zbl 1199.65306)