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Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators. (English) Zbl 1199.65306
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.
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
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