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Equivalence theorems for nonlinear finite-difference methods

  • II. Näherungsverfahren Für nichtlineare Anfangswertaufgaben Und Anfangsrandwertaufgaben
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Numerische Lösung nichtlinearer partieller Differential- und Integrodifferentialgleichungen

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

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References

  1. ANSORGE, R.: Konvergenz von Differenzenverfahren für quasilineare Anfangswertaufgaben. Numer. Math. 13, 217–225 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  2. ANSORGE, R., HASS, R.: Konvergenz von Differenzenverfahren für lineare und nichtlineare Anfangswertaufgaben. Lecture Notes in Mathematics 159. Berlin: Springer-Verlag 1970.

    MATH  Google Scholar 

  3. COLLATZ, L.: The numerical treatment of differential equations. Berlin: Springer-Verlag 1960.

    Book  MATH  Google Scholar 

  4. COLLATZ, L.: Funktionalanalysis und numerische Mathematik. Berlin: Springer-Verlag 1964.

    Book  MATH  Google Scholar 

  5. GODUNOV, S.K., RYABENKI, V.S.: Theory of difference schemes. Amsterdam: North-Holland publishing company 1964.

    MATH  Google Scholar 

  6. HASS, R.: Stabilität und Konvergenz von Differenzverfahren für halblineare Probleme. Thesis, Hamburg University 1971.

    Google Scholar 

  7. HENRICI, P.: Discrete variable methods in ordinary differential equations. New York: J. Wiley & Sons 1962.

    MATH  Google Scholar 

  8. HENRICI, P.: Elements of numerical analysis. New York: J. Wiley & Sons 1964.

    MATH  Google Scholar 

  9. JOHN, F.: On integration of parabolic equations by difference methods. Comm. Pure Appl. Math. 5, 155–211 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  10. KANTOROVICH, L.V., Akilov, G.P.: Functional analysis in normed spaces. Oxford: Pergamon Press 1964.

    MATH  Google Scholar 

  11. KINNEBROCK, W.: Stabilität und Konvergenz nichtlinearer Differenzenoperatoren bei Anfangswertaufgaben. Report, Gesellschaft für Kernforshung mbH Karlsruhe 1971.

    Google Scholar 

  12. RICHTMYER, R.D., MORTON, K.W.: Difference methods for initial-value problems. New York: John Wiley & Sons 1967.

    MATH  Google Scholar 

  13. SPIJKER, M.N.: Stability and convergence of finite-difference methods. Thesis, Leiden University 1968.

    Google Scholar 

  14. STETTER, H.J.: Asymptotic expansions for the error of discretization algorithms for nonlinear functional equations. Numer. Math. 7, 18–31 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  15. STETTER, H.J.: Stability of nonlinear discretization algorithms. In: Numerical solution of partial differential equations, ed. J.H. Bramble. New York: Academic Press 1966.

    Google Scholar 

  16. STRANG, W.G.: Difference methods for mixed boundary-value problems. Duke Math. J. 27, 221–231 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  17. STRANG, G.: Accurate partial difference methods II, Non-linear problems. Numer. Math. 6, 37–46 (1964).

    Article  MathSciNet  MATH  Google Scholar 

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R. Ansorge W. Törnig

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© 1972 Springer-Verlag Berlin · Heidelberg

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Spijker, M.N. (1972). Equivalence theorems for nonlinear finite-difference methods. 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/BFb0061621

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  • DOI: https://doi.org/10.1007/BFb0061621

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  • Print ISBN: 978-3-540-05895-3

  • Online ISBN: 978-3-540-37540-1

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