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Iterationsverfahren für elliptische (nichtlineare) Differenzenoperatoren in Divergenzform

III. Numerische Behandlung nichtlinearer Randwertprobleme

Part of the Lecture Notes in Mathematics book series (LNM,volume 267)

Abstract

Modifying a two-stage algorithm given by PETRYSHYN [11] and BREZISSIBONY

Teil einer modifizierten Fassung der Dissertation des Autors an der Universität München.

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Literatur

  1. AMES, W.: Nonlinear partial differential equations in engineering. Academic Press, New York (1965).

    MATH  Google Scholar 

  2. BELLMAN, R., KALABA, R.: Quasilinearization and nonlinear boundary value problems. Elsevier, New York (1965).

    MATH  Google Scholar 

  3. BREZIS, H., SIBONY, M.: Méthodes d'approximation de d'itération pour les opérateurs monotones. Arch.Rat.Mech.Anal. 28, 59–82 (1968).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. BROWDER, F.: The solvability of non-linear functional equations. Duke Math.J. 30, 557–566 (1963).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. COLLATZ, L.: Funktionalanalysis und numerische Mathematik. Springer, Berlin,Heidelberg,New York (1968).

    Google Scholar 

  6. D'YAKONOV, E.G.: On the solution of some elliptic difference equations. J.Inst.Maths Applics 7, 1–20 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. FREHSE, J.: Existenz und Konvergenz von Lösungen nichtlinearer elliptischer Differenzengleichungen unter DIRICHLET-Randbedingungen. Math.Z. 109, 311–343 (1969).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. KOSELEV, A.: Convergence of the method of successive approximation for quasilinear elliptic equations. Soviet Math.Dokl. 3, 219–222 (1962).

    MATH  Google Scholar 

  9. LADYSHENSKAYA, O., URAL'TSEVA, N.: Linear and quasilinear elliptic equations. Academic Press, New York (1968)

    Google Scholar 

  10. LEES, M.: Alternating direction and semi-explicit difference methods for parabolic differential equations. Num.Math. 3, 398–412 (1961).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. PETRYSHYN, W.: On the extension and the solution of non linear operator equations. Ill.J.Math. 10, 255–274 (1966).

    MathSciNet  MATH  Google Scholar 

  12. SAPAGOVAS, M.: The method of finite differences for the solution of quasilinear elliptic equations with discontinuous coefficients. USSR Comp.Math. and Math.Phys. 5, 72–85 (1965).

    CrossRef  Google Scholar 

  13. SERRIN, J.: The problem of DIRICHLET for quasilinear elliptic differential equations with many independent variables. Phil.Trans.Roy.Soc.London, Series A. 264, 413–496 (1969)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. SIBONY, M.: Méthodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone. Calcolo 7, 65–183 (1970).

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1972 Springer-Verlag Berlin · Heidelberg

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Sachs, A. (1972). Iterationsverfahren für elliptische (nichtlineare) Differenzenoperatoren in Divergenzform. In: Ansorge, R., Törnig, W. (eds) Numerische Lösung nichtlinearer partieller Differential- und Integrodifferentialgleichungen. Lecture Notes in Mathematics, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061624

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  • DOI: https://doi.org/10.1007/BFb0061624

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05895-3

  • Online ISBN: 978-3-540-37540-1

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