This is a preview of subscription content, log in via an institution to check access.
Literature Cited
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).
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).
N. N. Yanenko, The Method of Fractional Steps for the Solution of Multidimensional Problems of Mathematical Physics [in Russian], Nauka, Novosibirsk (1967).
S. G. Hahn, “Stability criteria for differences schemes,” Comm. Pure and Appl. Math.,11, No. 1, 243–255 (1958).
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).
K. O. Friedrichs, “Symmetric hyperbolic linear differential equations,” Comm. Pure and Appl. Math.,7, No. 2, 345–392 (1954).
P. D. Lax, “Differential equations, difference equations, and matrix theory,” Comm. Pure and Appl. Math.,11, No. 2, 175–194 (1958).
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.
N. N. Anuchina, “Some difference schemes for hyperbolic systems,” Trudy Matem. In-ta Akad. Nauk SSSR,74, 5–15 (1966).
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).
P. D. Lax, “Weak solutions of nonlinear hyperbolic equations and their numerical computation,” Comm. Pure and Appl. Math.,7, No. 1, 159–193 (1954).
N. N. Yanenko and Yu. I. Shokin, “On approximative viscosity in difference schemes,” Dokl. Akad. Nauk SSSR,182, No. 2, 280–281 (1968).
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).
P. D. Lax and B. Wendroff, “Systems of conservation laws. III,” Comm. Pure and Appl. Math.,13, No. 1, 217–238 (1960).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1966).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 5, pp. 1173–1187, September–October, 1969.
Rights and permissions
About this article
Cite this article
Yanenko, N.N., Shokin, Y.I. The first differential approximation to finite-difference schemes for hyperbolic systems of equations. Sib Math J 10, 868–880 (1969). https://doi.org/10.1007/BF00971662
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971662