References
P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (Soc. Ind. Appl. Math., Philadelphia, 1972).
B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Applications to Gas Dynamics (Nauka, Moscow, 1978; Am. Math. Soc., Providence, 1983).
V. Yu. Lyapidevskii and V. M. Teshukov, Mathematical Models of Long Wave Propagation in an Inhomogeneous Fluid (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].
A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Chapman and Hall/CRC, London, 2001).
V. V. Ostapenko, Hyperbolic Systems of Conservation Laws and Their Application to the Shallow Water Theory (Course of Lectures) (Novosibirsk, 2004) [in Russian].
L. V. Ovsyannikov, Prikl. Mekh. Tekh. Fiz., No. 2, 3–13 (1979).
P. E. Karabut and V. V. Ostapenko, Prikl. Mat. Mekh. 72, 958–970 (2009).
V. V. Ostapenko, Prikl. Mat. Mekh. 65, 94–113 (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.E. Karabut, V.V. Ostapenko, 2011, published in Doklady Akademii Nauk, 2011, Vol. 437, No. 1, pp. 9–15.
Rights and permissions
About this article
Cite this article
Karabut, P.E., Ostapenko, V.V. Method of successive approximations for the Riemann problem with a small-amplitude discontinuity. Dokl. Math. 83, 143–148 (2011). https://doi.org/10.1134/S1064562411020025
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562411020025