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On the convergence of the Godounov’s scheme for first order quasi linear equations. (English) Zbl 0372.35015


MSC:

35F20 Nonlinear first-order PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35A35 Theoretical approximation in context of PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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[1] E. Conway and J. Smoller: Global solutions of the Cauchy problem for quasi-linear first order equations in several space variables. Comm. Pure Applied Math., 19, 95-105 (1966). · Zbl 0138.34701
[2] E. Hopf: On the right weak solution of the Cauchy problem for a quasi-linear equation of first order. J. Math. Mech., 19, 483-487 (1969). · Zbl 0188.16102
[3] S. N. Kruzkov: First order quasi-linear equations in several independant variables. Math. USSR Sbornik., 10, 217-243 (1970). · Zbl 0215.16203
[4] A. Y. Le Roux: Resolution numerique du probleme de Cauchy pour une equation quasilineaire du premier ordre a une ou plusieurs variables d’espaces. These de 3eme cycle-Rennes (1974).
[5] A. Y. Le Roux: a numerical conception of entropy for quasi-linear hyperbolic equations (to appear in Math. Comp.) · Zbl 0378.65053
[6] O. A. Oleinik: Discontinuous solutions of non linear differential equations. AMS transl. Ser. 2, n^\circ 26, pp. 95-172 (1963). · Zbl 0131.31803
[7] O. A. Oleinik: Uniqueness and Stability of the generalized solution of the Cauchy problem for a quasi-linear equation. AMS transl., Ser. 2, n^\circ 33, pp. 285-290 (1963). · Zbl 0132.33303
[8] R. D. Richtmyer and K. W. Morton: Difference Methods for Initial Value Probelms. J. Wiley (1967). · Zbl 0155.47502
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