Geodesic
Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators
Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1
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It is obtained estimates of stability with respect to perturbation of operator for solution of the first- and second-order differential-operator equations. For two- and three-level operator-difference schemes with weights similar estimates holds. Using the obtained results we construct the estimates of coefficient stability for one-dimensional parabolic and hyperbolic equations as well as for the difference schemes approximating the corresponding differential problems. 
@article{KJM_2007_30_1_a4,
     author = {B. S. Jovanovi\'c and S. V. Lemeshevsky and P. P. Matus and P. N. Vabishchevich},
     title = {Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators},
     journal = {Kragujevac Journal of Mathematics},
     pages = {59 - 88},
     year = {2007},
     volume = {30},
     number = {1},
     zbl = {1199.65306},
     url = {http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a4/}
}
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B. S. Jovanović; S. V. Lemeshevsky; P. P. Matus; P. N. Vabishchevich. Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators. Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1. http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a4/