References
Collatz, L.: The numerical treatment of differential equations, 3rd edit.: Springer 1960.
Dahlquist, G.: Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand.4, 33–53 (1956).
Dahlquist, G.: Stability and error bounds in the numerical integration of ordinary differential equations. Trans. Roy. Inst. Tech. Stockholm No. 130 (1959).
Forsythe, G., andW. Wasow: Finite-difference methods for partial differential equations. New York: Wiley 1960.
Moore, R.: A Runge-Kutta procedure for the Goursat problem in hyperbolic partial differential equations. Arch. Rational Mech. Anal.7, 37–63 (1961).
Thomas, L.: Computation of one-dimensional compressible flows including shocks. Comm. Pure Appl. Math.7, 195–206 (1954).
Sauer, R.: Anfangswertprobleme bei partiellen Differentialgleichungen 2. Aufl. Berlin-Göttingen-Heidelberg: Springer 1958.
Courant, R., u.D. Hilbert: Methoden der mathematischen Physik, Bd. 2. Berlin: Springer 1937.
Douglis, A.: Some existence theorems for hyperbolic systems of partial differential equations in two independent variables. Comm. Pure Appl. Math.5, 119–154 (1952).
Friedrichs, K., u.H. Lewy: Das Anfangswertproblem einer beliebigen nichtlinearen hyperbolischen Differentialgleichung. Math. Ann.99, 200–221 (1928).
Beckert, H.: Existenz- und Eindeutigkeitsbeweise für das Differenzenverfahren zur Lösung des Anfangswertproblems... Ber. Verh. Sächs. Akad. Wiss.97, H. 4 (1950).
Ralston, A., andH. Wilf: Mathematical methods for digital computers. New York: Wiley 1960.
Seegmüller, G.: Error analysis for the numerical solution of certain differential equations in gasdynamics, Proceedings, Symposium on the numerical treatment of ord. differential equations, 20.–24. Sept. 1960, Rome.
Gelfond, A.: Differenzenrechnung, Deutsch. Verl. Wiss., 1958.
Lax, P., andR. Richtmyer: Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math.9, 267–293 (1956).
Hartree, D.: Numerical Analysis, 2nd edit. Oxford: Clarendon Press 1958.
Liniger, W.: Zur Stabilität der numerischen Integrationsmethoden für Differentialgleichungen. Dissertation Lausanne 1956.
Richardson, C., andJ. Gaunt: The deferred approach to the limit. Trans. Roy. Soc. Lond.226, 300–361 (1927).
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Von der Fakultät für Allgemeine Wissenschaften der Technischen Hochschule München angenommene Habilitationsschrift.
This research was supported in part by the AFOSR of the Air Research and Development Command, European Office, under Grant No. AF-EOARDC-61-21.
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Stetter, H.J. On the convergence of characteristic finite-difference methods of high accuracy for quasi-linear hyperbolic equations. Numer. Math. 3, 321–344 (1961). https://doi.org/10.1007/BF01386033
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DOI: https://doi.org/10.1007/BF01386033