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Warianty tytułu
Abstrakty
CONTENTS
Introduction......................................................................................................................................... 5
§ 1. A maximum principle for linear mappings.................................................................................... 6
§ 2. A maximum principle for nonlinear mappings............................................................................. 9
§ 3. A finite difference analogue of a maximum principle for nonlinear elliptic equations.......... 11
§ 4. A finite difference scheme of higher order accuracy.................................................................... 16
§ 5. A maximum principle for systems of ordinary differential equations....................................... 23
§ 6. The method of lines for nonlinear parabolic equations which can be degenerated
to elliptic equations.................................................................................................................................... 27
§7. A geometrical interpretation of a maximum principle for a system of difference
equations..................................................................................................................................................... 30
§8. A strong maximum principle for an elliptic system of nonlinear equations............................. 33
References.................................................................................................................................................. 41
Introduction......................................................................................................................................... 5
§ 1. A maximum principle for linear mappings.................................................................................... 6
§ 2. A maximum principle for nonlinear mappings............................................................................. 9
§ 3. A finite difference analogue of a maximum principle for nonlinear elliptic equations.......... 11
§ 4. A finite difference scheme of higher order accuracy.................................................................... 16
§ 5. A maximum principle for systems of ordinary differential equations....................................... 23
§ 6. The method of lines for nonlinear parabolic equations which can be degenerated
to elliptic equations.................................................................................................................................... 27
§7. A geometrical interpretation of a maximum principle for a system of difference
equations..................................................................................................................................................... 30
§8. A strong maximum principle for an elliptic system of nonlinear equations............................. 33
References.................................................................................................................................................. 41
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
183
Liczba stron
41
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXXIII
Daty
wydano
1981
Twórcy
autor
Bibliografia
- [1] I. H. Bramble and В. E. Hubbard, On a finite difference analogue of an elliptic boundary problem which is neither diagonally dominant nor of non-negative type, J. Math, and Phys. 43 (1964). pp. 117-132.
- [2] E. Hopf, Elementare Betrachtung über die Losüngen partieller Differentialgleichungen zweiter Ordnung von elliptischen Typus, Sitzungsberichte Preuss. Acad. Wiss. 19 (1927), pp. 147-152.
- [3] M. Krzyżański, Równania różniczkowe cząstkowe rzędu drugiego, Część I, Warszawa 1957.
- [4] R. M. Redheffer, An extension of certain maximum principle, Monatch. Math. 6 (1962), pp. 32-42.
- [5] I. A. Rus, Un principle du maximum pour les solutions d'un système fortment elliptique, Glasnik Mat. Ser. Ill 4 (24) (1969). pp. 75-77.
- [6] А. А. Самарский, Введение а теорию разностных схем, Москва 1971.
- [7] W. J. Skorobogatko, Studying in Qualitative Theory of Differential Partial Equations, Izdatielstwo Lvovskogo Universiteta, Lvov 1961.
- [8] T. Styś, A maximum principle for systems of ordinary differential equations, Bull, Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1977), pp. 875-878.
- [9] T. Styś, The method of lines for nonlinear parabolic equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1977), pp. 207-210.
- [10] T. Styś, On the maximum principle for certain system of difference equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 10 (1971), pp. 963-966.
- [11] T. Styś, The maximum principle for system of nonlinear differential equations of the Monge- Ampere type. Lecture Notes in Math. 395 (1974), pp. 235-243.
- [12] T. Styś, On a maximum principle for nonlinear equations, Banach Center Publications, v. 3, Mathematical Models and Numerical Methods, Warszawa (1978), pp. 69-78.
- [13] T. Styś, Aprioristic estimations of solutions of certain elliptic system of partial differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom Phys. 9 (1965), pp. 639-640.
- [14] T. Styś, Zasada maksimum dla pewnych układów równań różniczkowych, Warszawa 1968.
- [15] W. Walter, Differential and Integral Inequalities, Springer-Verlag, Berlin-Heidelberg-New York 1970.
- [16] A. Wakulicz, Metodi alle differenze per equazioni differenziali alle derivate parziali, Roma 1970.
- [17] R. S. Varga, On a discrete maximum principle, SIAM J. Numer. 3 (1966), pp. 335-339.
- [18] D. M. Young, Iterative solution of large linear systems. New York 1971.
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