Systems of Conservation Laws

Communications on Pure and Applied MathematicsVolume 13, Issue 2 p. 217-237 Article Systems of conservation laws† Peter Lax, Peter Lax New York University and Los Alamos Scientific LaboratorySearch for more papers by this authorBurton Wendroff, Burton Wendroff New York University and Los Alamos Scientific LaboratorySearch for more papers by this author Peter Lax, Peter Lax New York University and Los Alamos Scientific LaboratorySearch for more papers by this authorBurton Wendroff, Burton Wendroff New York University and Los Alamos Scientific LaboratorySearch for more papers by this author First published: May 1960 https://doi.org/10.1002/cpa.3160130205Citations: 1,684 † This paper represents results obtained under the sponsorship of the U.S. Atomic Energy Commission, Contract W-7405-ENG 36. Reproduction in whole or in part permitted for any purpose of the United States Government. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Courant, R., and Friedrichs, K. O., Supersonic Flow and Shock Waves, Interscience Publishers, New York, 1948. 2 Courant, R., Friedrichs, K. O., and Lewy, H., Über die Partiellen Differenzengleichungen der Mathematischen Physik, Math. Ann., Vol. 100, 1928, pp. 32–74. 3 Harlow, F. H., Hydrodynamic problems involving large fluid distortions, J. Assoc. Comp. Mach., Vol. 4, 1957, pp. 137–142. 4 John, F., On integration of parabolic equations by difference methods, Comm. Pure Appl. Math., Vol. 5, 1952, pp. 155–211. 5 Landshoff, R., A numerical method for treating fluid flow in the presence of shocks, Los Alamos Scientific Laboratory Report LA-1930, January, 1955. 6 Lax, P. D., On discontinuous initial value problems for nonlinear equations and finite difference schemes, Los Alamos Scientific Laboratory Report LAMS-1332, December, 1952. 7 Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., Vol. 7, 1954, pp. 159–193. 8 Lax, P. D., On the scope of the energy method, Bull. Amer. Math. Soc., Vol. 66, 1960, pp. 32–35. 9 Lax, P. D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., Vol. 10, 1957, pp. 537–566. 10 Lax, P. D., and Richtmyer, R. D., Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math., Vol. 9, 1956, pp. 267–293. 11 Longley, H. J., Methods of differencing in Eulerian hydrodynamics, Los Alamos Scientific Laboratory Report, LAMS-2379. 12 Von Neumann, J., Proposal and analysis of a numerical method for the treatment of hydro-dynamical shock problems, National Defense and Research Committee Report AM-551, March, 1944. 13 Von Neumann, J., and Richtmyer, R. D., A Method for the numerical calculations of hydrodynamic shocks, J. Appl. Physics, Vol. 21, 1950, pp. 232–237. 14 Godunov, S. K., Difference method for the numerical computation of discontinuous solutions of equations of hydrodynamics, Mat. Sbornik, N. S., Vol. 47 (89), No. 3, 1959, pp. 271–306. 15 Lax, P. D., On difference schemes for solving initial value problems for conservations laws, Symposium on Questions of Numerical Analysis, Provisional International Computing Center, Rome, 1958, pp. 69–78. Citing Literature Volume13, Issue2May 1960Pages 217-237 ReferencesRelatedInformation