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A Priori Estimates for Some Classes of Difference Schemes

Published online by Cambridge University Press:  20 November 2018

Nikolai Bakaev*
Affiliation:
Millionschikova, 11, Kv. 82 Moscow 115487 Russia, bakaev@wiamath.msk.su
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Abstract

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A new approach to the analysis of the well-posedness of difference parabolic problems is proposed, which is based on weaker assumptions than in earlier works. The results are applied to the study of multi-dimensional difference parabolic problems in mesh Lebesgue spaces.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Bakaev, N.Yu., Stability estimates for a certain general discretization method, Dokl. Akad. Nauk. SSSR 309 (1989), 1115.Google Scholar
2. Bakaev, N.Yu., On the theory of difference operators in the spaces Lph, VANT, Ser. Mat. Modelir. Fizich. Protsz. (1992), 1820.Google Scholar
3. Bakaev, N.Yu., A priori estimates for certain classes of multidimensional difference initial-boundary-value problems, Zh. Vychisl. Mat i Mat. Fiz. 33 (1993), 795-S04.Google Scholar
4. Bakaev, N.Yu., Stability estimates of difference schemes for a differential equation with constant operator. II, Imbedding theorems and their Appl. to Math. Phys. Probl., Novosibirsk, SO AN SSSR (1989), 1837.Google Scholar
5. Bakaev, N.Yu., Stability estimates of difference schemes for a differential equation with constant operator. I, Partial Differential Equations, Novosibirsk, SO AN SSSR (1989), 314.Google Scholar
6. Brenner, Ph. and Thomee, V., On rational approximations of semigroups, SIAM J. Numer. Anal. 16 (1979), 683694.Google Scholar
7. Butcher, J.C., Implicit Runge-Kutta processes, Math. Comput 18 (1964), 5064.Google Scholar
8. Crouzeix, M., On multistep approximations of semigroups in Banach spaces, J. Comput. Appl. Math. 20 (1987), 2536.Google Scholar
9. Crouzeix, M., Larsson, S., Piskarev, S. and Thomee, V., The stability of rational approximations of analytical semigroups, BIT 33 (1993), 7484.Google Scholar
10. Dekker, K. and Verwer, J.G.,Stability of Runge-Kutta methods for stiff nonlinear differential equations, North Holland, Amsterdam, New York, Oxford, 1984.Google Scholar
11. Evgraphov, M.A.,Asymptotic estimates and entire functions, Moscow, Nauka, 1979.Google Scholar
12. Krein, S.G.,Linear differential equations in Banach space, Moscow, Nauka, 1967.Google Scholar
13. Lubich, Ch. and Ostermann, A., Runge-Kutta methods for parabolic equations and convolution quadrature, Math. Comput. 60 (1993), 105131.Google Scholar
14. Palencia, C., A stability result for sectorial operators in Banach spaces, SIAM J. Numer. Anal. 30 (1993), 13731384.Google Scholar
15. Palencia, C., On the stability of variable stepsize rational approximations of holomorphic semigroups, Math. Comput. 62 (1994), 93103.Google Scholar
16. Privalov, I.I.,An introduction to the theory of functions in a complex variable, Moscow, Nauka, 1984.Google Scholar
17. Samarskii, A.A.,The theory of difference schemes, Moscow, Nauka, 1983.Google Scholar
18. Samarskii, A.A. and Goolin, A.V.,The stability of difference schemes, Moscow, Nauka, 1973.Google Scholar
19. Triebel, H.,Interpolation theory. Function spaces. Diferential operators, Berlin, VEB Deutscher Verlag, 1978.Google Scholar
20. Vinokurov, V.A. and Iuvchenko, N.V., Semi-explicit numerical methods for solving stiff problems, Dokl. Akad. Nauk. SSSR 284 (1985), 272277.Google Scholar