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On existence, uniqueness, and numerical evaluation of solutions of ordinary and hyperbolic differential equations. (English) Zbl 0100.29202


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[1] Picard, E.,Sur les méthodes d’approximations successives dans la théorie des équations différentielles, (Note I to vol. 4 ofG. Darboux,Lecons sur la Théorie Générale des Surfaces, Paris, 1896, pp. 353-367).
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[8] Moore, R. H.,Proof of an existence and uniqueness theorem of Picard for a non-linear hyperbolic partial differential equation, M. A. thesis, University of Maryland, June, 1955.
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[11] Diaz, J. B., On an analogue of the Euler-Cauchy polygon method for the numerica-solution of uxy = f(x, y, u, u_x, u_y), Archive for Rational Mechanics and Analysis, 1, 357-390 (1958) · Zbl 0084.11501 · doi:10.1007/BF00298015
[12] Guglielmino; Francesco, Sulla risoluzione del problema di Darboux per l’equazione s = f(x, y, z), Boll. Unione Mat. Italiana, 13, 3, 308-318 (1958) · Zbl 0084.29602
[13] Villari; Gaetano, Su un problema al contorno per l’equazione classe di sistemi di eguazione alle derivate parziali, Boll. Unione Mat. Italiana, 13, 3, 1-8 (1958) · Zbl 0088.07102
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[16] Moore, R. H.,On approximation of the solutions of the Goursat problem for second order quasi-linear equations, Ph. D. thesis, University of Michigan, June 1959 (to appear in the Archive for Rational Mechanics and Analysis).
[17] Santoro; Paolo, Sul problema di Darboux per l’equazione s = f(x, y, z, p, q) e il fenomeno di Peano, Rendiconti dell’Accademia Nazionale dei XL, X, 82, 3-17 (1959)
[18] Walter, W., Eindeutigkeitssatze fur die Differentialgleichung u_xy = f(x, y, u, u_x, u_y), Math. Zeit., 71, 398-324 (1959) · Zbl 0088.07402
[19] Billings, J. H.,Extensions of the Laplace method, Ph. D. thesis, University of Mary, land, June 1960 (see also Technical Note BN-209, University of Maryland, 1960).
[20] Sternberg, H. M.,The solution of the characteristic and the Cauchy problems for the Bianchi partial differential equation in n independent variables by a generalization of Riemann’s method, Ph. D. thesis, University of Maryland, June 1960.
[21] Aziz, A. K., andDiaz, J. B.,On higher order boundary value problems for a linear hyperbolic partial differential equation in three independent variables (to appear in the Indiana Journal of Mathematics and Mechanics). · Zbl 0095.07603
[22] Shanahan, John, P.,On uniqueness questions for hyperbolic differential equations (to appear in the Pacific Journal of Mathematics). · Zbl 0098.29502
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