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The first differential approximation to finite-difference schemes for hyperbolic systems of equations. (English) Zbl 0196.11701


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[1] N. N. Yanenko and Yu. I. Shokin, ?On the correctness of the first differential approximations to difference schemes,? Dokl. Akad. Nauk SSSR,182, No. 4, 776-778 (1968). · Zbl 0191.11002
[2] N. N. Yanenko and Yu. I. Shokin, ?On the connection between the correctness of the first differential approximations and the stability of difference schemes for hyperbolic systems of equations,? Matem. Zametki,4, No. 5, 493-502 (1968).
[3] N. N. Yanenko, The Method of Fractional Steps for the Solution of Multidimensional Problems of Mathematical Physics [in Russian], Nauka, Novosibirsk (1967). · Zbl 0183.18201
[4] S. G. Hahn, ?Stability criteria for differences schemes,? Comm. Pure and Appl. Math.,11, No. 1, 243-255 (1958). · Zbl 0082.12301 · doi:10.1002/cpa.3160110207
[5] N. N. Yanenko and Yu. I. Shokin, ?Approximative viscosity in difference schemes for hyperbolic systems of equations,? in: Proceedings of the All-Union Seminar on Numerical Methods in the Mechanics of Viscous Liquids [in Russian], Nauka, Novosibirsk (1969).
[6] K. O. Friedrichs, ?Symmetric hyperbolic linear differential equations,? Comm. Pure and Appl. Math.,7, No. 2, 345-392 (1954). · Zbl 0059.08902 · doi:10.1002/cpa.3160070206
[7] P. D. Lax, ?Differential equations, difference equations, and matrix theory,? Comm. Pure and Appl. Math.,11, No. 2, 175-194 (1958). · Zbl 0086.01603 · doi:10.1002/cpa.3160110203
[8] N. N. Yanenko, ?Some aspects of the theory of convergence of difference schemes with constant and variable coefficients,? in: Proceedings of the Fourth All-Union Mathematical Congress, Vol. 2 [in Russian], Leningrad (1964), pp. 612-621.
[9] N. N. Anuchina, ?Some difference schemes for hyperbolic systems,? Trudy Matem. In-ta Akad. Nauk SSSR,74, 5-15 (1966).
[10] Yu. I. Shokin, ?On the connection between the correctness of the first differential approximations and the stability of some difference schemes,? in: Proceedings of the All-Union Seminar on Numerical Methods in the Mechanics of Viscous Fluids [in Russian], Nauka, Novosibirsk (1969).
[11] P. D. Lax, ?Weak solutions of nonlinear hyperbolic equations and their numerical computation,? Comm. Pure and Appl. Math.,7, No. 1, 159-193 (1954). · Zbl 0055.19404 · doi:10.1002/cpa.3160070112
[12] N. N. Yanenko and Yu. I. Shokin, ?On approximative viscosity in difference schemes,? Dokl. Akad. Nauk SSSR,182, No. 2, 280-281 (1968).
[13] Yu. I. Shokin, ?On approximative viscosity in implicit difference schemes,? in: Proceedings of the All-Union Seminar on Numerical Methods in the Mechanics of Viscous Fluids [in Russian], Nauka, Novosibirsk (1969).
[14] P. D. Lax and B. Wendroff, ?Systems of conservation laws. III,? Comm. Pure and Appl. Math.,13, No. 1, 217-238 (1960). · Zbl 0152.44802 · doi:10.1002/cpa.3160130205
[15] F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1966). · Zbl 0050.24804
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