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Kreiss, H.-O.

Über die Stabilitätsdefinition für Differenzengleichungen, die partielle Differentialgleichungen approximieren. (German) Zbl 0109.34702

BIT, Nord. Tidskr. Inf.-behandl. 2, 153-181 (1962).
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Cited in 5 Reviews
Cited in 70 Documents

Keywords:

numerical analysis
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\textit{H. O. Kreiss}, BIT, Nord. Tidskr. Inf.-behandl. 2, 153--181 (1962; Zbl 0109.34702)
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References:

[1] G. E. Forsythe and W. R. Wasow,Finite-Difference Methods For Partial Differential Equations. John Wiley & Sons, New York 1960. · Zbl 0099.11103
[2] P. D. Lax and R. D. Richtmyer,Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math., 9 (1956), 267–293. · Zbl 0072.08903
[3] P. D. Lax,Differential equations, difference equations and matrix theory. Comm. Pure Appl. Math., 11 (1958), 175–194. · Zbl 0086.01603
[4] L. Gårding,Linear hyperbolic partial differential equations with constant coefficients. Acta Math., 85 (1951), 1–62. · Zbl 0045.20202
[5] V. S. Ryabenkii und A. F. Filippow,Über die Stabilität von Differenzengleichungen. Deutscher Verlag der Wissenschaften, Berlin 1960.
[6] G. Dahlquist,Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand., 4 (1956), 33–53. · Zbl 0071.11803
[7] F. John,On integration of parabolic equations by difference methods. Comm. Pure Appl. Math., 5 (1952), 155–211. · Zbl 0047.33703
[8] K. O. Friedrichs,Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math., 7 (1954), 345–392. · Zbl 0059.08902
[9] H. O. Kreiss, Über die Lösung des Cauchyproblems für lineare partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. Acta Math., 101 (1959), 179–199. · Zbl 0087.29901
[10] H. O. Kreiss, Über die Differenzapproximation hoher Genauigkeit bei Anfangswertproblemen für partielle Differentialgleichungen. Num. Math., 1 (1959), 186–202. · Zbl 0092.13002
[11] P. D. Lax, On the stability of difference approximations to solutions of hyperbolic equations with variable coefficients. Comm. Pure Appl. Math., 14 (1961), 497–520. · Zbl 0102.11701
[12] P. D. Lax and B. Wendroff, On the stability of difference schemes. Manuskript. · Zbl 0113.32301
[13] I. Petrovskii, Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen im Gebiete der nichtanalytischen Funktionen. Bull. Univ. Etat. Moscou Ser. Int. Sect. A Fasc. 7 (1938), 1–74.
[14] W. G. Strang,Difference methods for mixed boundary-value problems. Duke Math. Journal, 27 (1960), 221–232. · Zbl 0091.26904
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