## On approximate solutions of non-linear hyperbolic partial differential equations.(English)Zbl 0099.33604

### Keywords:

numerical analysis
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 [1] Arzelà, C.: Sull’esistenza degli integrali delle equazioni differenziali ordinarie. Mem. Reale Accad. Sci. Inst. Bologna, Ser. V, 6, 131–140 (1896). [2] Conlan, J.: The Cauchy problem and the mixed boundary value problem for a non-linear hyperbolic partial differential equation in two independent variables. Arch. rational Mech. Anal. 3, 355–380 (1959). · Zbl 0093.31203 [3] Diaz, J. B.: On an analogue of the Euler-Cauchy polygon method for the numerical solution of u xy=f(x, y, u, ux, uy). Arch. rational Mech. Anal. 1, 357–390 (1958). · Zbl 0084.11501 [4] Goursat, E.: Cours D’Analyse, vol. 1, p. 43. Paris: Gauthier-Villars 1943. · JFM 46.0375.13 [5] Hartman, P., & A. Wintner: On hyperbolic partial differential equations. Amer. J. Math. 74, 834–864 (1952). · Zbl 0048.33302 [6] Kutta, W.: Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Z. Math. Phys. 46, 435–453 (1901). · JFM 32.0316.02 [7] Leehey, P.: On the existence of not necessarily unique solutions of classical hyperbolic boundary value problems for non-linear second order partial differential equations in two independent variables. Ph. D. Thesis, Brown University, June 1950. [8] Mie, G.: Beweis der Integrierbarkeit gewöhnlicher Differentialgleichungssysteme nach Peano. Math. Ann. 43, 553–586 (1893). (This is a summary in German of Peano’s paper [9], much of which is written in logical notation.) · JFM 25.0504.01 [9] Peano, G.: Démonstration de l’intégrabilité des équations différentielles ordinaires. Math. Ann. 37, 182–228 (1890). (Cf. Mie [8] above.) · JFM 22.0302.01 [10] Zwirner, G.: Sull’approssimazione degli integrali del sistema differenziale $$\frac{{\partial ^2 z}}{{\partial x\partial y}} = f(x, y, z ), z(x_0 , y) = \psi (y), z(x, y_0 ) = \varphi (x)$$ . Atti dell’ Istituto Veneto di Scienze, Lettere ed Arti, Cl. Sci. Fis. Mat. Nat. 109, 219–231 (1950, 51).
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