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Über die Lösung des Cauchyproblems für Lineare Partielle Differentialgleichungen mit Hilfe von Differenzengleichungen

Teil 1: Stabile Systeme von Differenzengleichungen

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Acta Mathematica

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Literatur

  1. Courant, R., Friedrichs, K. O. &Lewy, H., Über die partiellen Differenzengleichungen der mathematischen. Physik.Math. Ann., 100 (1928), 32–74.

    MathSciNet  Google Scholar 

  2. Friedrichs, K. O., Symmetric hyperbolic linear differential equations.Comm. Pure Appl. Math., 7 (1954), 345–392.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Kreiss, H. O., Über sachgemässe Cauchyprobleme für Systeme von linearen partiellen Differentialgleichungen.Transactions of the Royal Institute of Technology, Stockholm, Nr 127 (1958).

  5. Kreiss, H. O., Über die approximative Lösung von linearen partiellen Differentialgleichungen mit Hilfe von Differenzengleichungen.Transactions of the Royal Institute of Technology, Stockholm, Nr 128 (1958).

  6. Lax, P. D., Differential equations, difference equations and matrix theory.Comm. Pure Appl. Math., 11 (1958), 175–194.

    Article  MATH  MathSciNet  Google Scholar 

  7. Lax, P. D. &Richtmyer, R. D., Survey of the stability of linear finite difference equations.Comm. Pure Appl. Math., 9 (1956), 267–293.

    Article  MATH  MathSciNet  Google Scholar 

  8. Leray, J., (A) Lectures on hyperbolic equations with variable coefficients.Princeton, Institute for Advanced Studies, Fall. 1952. (B) On linear hyperbolic equations with variable coefficients on vector spaces.Princeton, Annals of Mathematics Studies, Vol. 33, 1954.

    Google Scholar 

  9. Měimann, N. N., On the theory of partial differential equations.Doklady Akad. Nauk SSSR (NS), 97 (1954), 593–596.

    Google Scholar 

  10. v. Neumann, J. &Richtmyer, R. D., A method for numerical calculation of hydrodynamic shocks.J. Appl. Phys., 21 (1950), 232–237.

    Article  MATH  MathSciNet  Google Scholar 

  11. O'Brien, G. G., Hyman, M. A. &Kaplan, S. A., A study of numerical solution of partial differential equations.J. Math. Phys., 29 (1951), 211–251.

    MathSciNet  Google Scholar 

  12. Rýabenkii, V. S., On the application of the method of finite differences to the solution of Cauchy's problem.Doklady Akad. Nauk SSSR (NS), 86 (1952), 1071–1074.

    Google Scholar 

  13. Todd, J., A direct approach to the problem of stability in the numerical solution of partial differential equations.Comm. Pure Appl. Math., 9 (1956), 597–612.

    Article  MATH  MathSciNet  Google Scholar 

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  1. Stockholm

    Heinz-Otto Kreiss

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  1. Heinz-Otto Kreiss
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Teil 2 folgt in Kürze.

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Kreiss, HO. Über die Lösung des Cauchyproblems für Lineare Partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. Acta Math. 101, 179–199 (1959). https://doi.org/10.1007/BF02559554

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