Abstract For the solutions of a nonlinear second-order differential-operator equation and the corresponding three-level operator-difference scheme, we establish sufficient boundedness conditions as well as sufficient conditions for the stability with respect to perturbations of the operators. These results are applied to studying the coefficient stability of a mixed problem for a hyperbolic equation with damping and a three-level difference scheme approximating this problem.

中文翻译：

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二阶微分算子方程及其差分近似解的稳定性

摘要 对于非线性二阶微分算子方程的解和相应的三级算子差分格式，我们建立了充分有界条件以及算子扰动稳定性的充分条件。这些结果用于研究带阻尼的双曲方程的混合问题的系数稳定性和近似该问题的三水平差分格式。