Bibliography
J. Diaz,On an analogue of the Euler-Cauchy polygon method for the numerical solution of u xy =f(x, y, u, u x ,u y ), Arch. Rat. Mech. Anal.1 (1957), 154–180.
R. H. Moore,A Runge-Kutta procedure for the Goursat problem in hyperbolic partial differential equations, Arch. Rat. Mech. Anal. 7 (1961), 37–63.
W. Törnig,Zur numerischen Behandlung von Anfangswertproblemen partieller hyperbolischer Differentialgleichungen zweiter Ordnung in zwei unabhängigen Veränderlichen, part I & II, Arch. Rat. Mech. Anal. 4 (1960), 428–466.
P. Henrici,Discrete variable methods in ordinary differential equations, Wiley u. Sons, 1962.
H. J. Stetter,Maximum bounds for the solutions of initial value problems for partial difference equations, Num. Math. 5 (1963), 399–424.
R. D. Richtmyer,Difference methods for initial value problems, Interscience Publ., 1957.
H. J. Stetter,On the convergence of characteristic finite-difference methods of high accuracy for quasi-linear hyperbolic equations, Num. Math. 3 (1961), 321–344.
G. Dahlquist,Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand. 4, 33–53 (1956).
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During some phases of the preparation of this paper, the first author was supported in part by the AFOSR, European Office, under Grant No. AF-EOARDC 63-77; the paper was completed under the sponsorship of the Office of Naval Research, US Navy, while the first author was working at the University of California, Los Angeles (Numerical Analysis Research).
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Steeter, H.J., Törnig, W. General multistep finite difference methods for the solution ofu xy =f(x, y, u, u x ,u y ). Rend. Circ. Mat. Palermo 12, 281–298 (1963). https://doi.org/10.1007/BF02851264
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DOI: https://doi.org/10.1007/BF02851264