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

Author:

Lemeshevsky S. V.,Matus P. P.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics,Analysis

Reference11 articles.

1. Levine, H.A., Instability and nonexistence of global solutions to nonlinear wave equations of the form $$Pu_{tt}=-Au+F(u)$$,Trans. Am. Math. Soc., 1974, vol. 192, pp. 1–21.

2. Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1977.

3. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P., Strong stability of differential-operator and operator-difference schemes, Dokl. Ross. Akad. Nauk, 1997, vol. 356, no. 4, pp. 455–457.

4. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P., Coefficient stability of differential-operator and operator-difference schemes, Mat. Model., 1998, vol. 10, no. 8, pp. 103–113.

5. Matus, P.P., Lemeshevsky, S.V., and Kandratsiuk, A.N., Well-posedness and blow up for IBVP for semilinear parabolic equations and numerical methods, Comp. Methods Appl. Math., 2010, vol. 10, no. 4, pp. 395–421.

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