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Numerical methods and existence theorems for ordinary differential equations. (English) Zbl 0089.29003


MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
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References:

[1] Dahlquist, Germund: Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand.4, 33-53 (1956).?Stability and error bounds in the numerical integration of ordinary differential equations. Diss. Stockholm 1958. · Zbl 0071.11803
[2] Ince, E. L.: Ordinary differential equations, Sect. 3/4. London: Longmans, Green & Co., 1927 and New York: Dover Publications.
[3] John, F.: On the integration of parabolic equations by difference methods. Communications Pure and Appl. Math.5, 155-211 (1952). · Zbl 0047.33703 · doi:10.1002/cpa.3160050203
[4] Lipschitz, R.: Sur la possibilité d’intégrer complètement un système donné d’équations différentielles. Bull. Sci. Math.10, 149-159 (1876).
[5] Moigno, F. N. M.: Leçons de calcul, 2, p., 385 and 513. Paris: Gauthier-Villars 1844.
[6] Osgood, W. F.: Beweise der Existenz einer Lösung der Differentialgleichungdy/dx=f(x, y) ohne Hinzunahme der Cauchy-Lipschitz-Bedingung. Mh. Math u. Physik9, 331-345 (1898). · JFM 29.0260.03
[7] Peano, G.: Démonstration de l’intégrabilité des équations differentielles ordinaires. Math. Ann.37, 182-228 (1890). · JFM 22.0302.01 · doi:10.1007/BF01200235
[8] Richtmyer, R. D.: Difference methods for initial value problems, Chapt. 3. New York: Interscience Publishers, Inc. · Zbl 0079.33702
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