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Finite difference methods for nonlinear hyperbolic systems


Authors: A. R. Gourlay and J. Ll. Morris
Journal: Math. Comp. 22 (1968), 28-39
MSC: Primary 65.67
DOI: https://doi.org/10.1090/S0025-5718-1968-0223114-8
MathSciNet review: 0223114
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  • [1] S. Z. Burstein, Numerical Calculations of Multidimensional Shocked Flows, N.Y.U. Courant Inst. Math. Sci. Res. Dep. N.Y.O.-10, 433, 1963.
  • [2] R. Courant, K. O. Friedrichs & H. Lewy, On the Partial Difference Equations of Mathematical Physics, translated from German by Phyllis Fox, N.Y.U. Courant Inst. Math. Sci. Res. Dep. N.Y.O.-7689, 1956.
  • [3] G. Ye. D'jakonov, "Difference schemes with a disintegrating operator for multi-dimensional problems," translated from the Russian, U.S.S.R. Comp. Math, and Math. Physics, v. 4, 1964, pp. 581-607.
  • [4] J. Gary, "On certain finite difference schemes for hyperbolic systems," Math. Comp., v. 18, 1964, pp. 1-18. MR 28 #1776. MR 0158553 (28:1776)
  • [5] A. R. Gourlay & A. R. Mitchell, "A stable implicit difference method for hyperbolic systems in two space variables," Numer. Math., v. 8, 1966, pp. 367-375. MR 33 #6850.
  • [6] P. D. Lax & B. Wendroff, "Systems of conservation laws," Comm. Pure Appl. Math., v. 13, 1960, pp. 217-237. MR 22 #11523. MR 0120774 (22:11523)
  • [7] P. D. Lax & B. Wendroff, "Difference schemes for hyperbolic equations with high order of accuracy," Comm. Pure Appl. Math., v. 17, 1964, pp. 381-398. MR 30 #722. MR 0170484 (30:722)
  • [8] P. D. Lax & R. D. Richtmyer, "Survey of the stability of linear finite difference equations," Comm. Pure Appl. Math., v. 9, 1956, pp. 267-293. MR 18, 48. MR 0079204 (18:48c)
  • [9] S. V. Parter, "Stability, convergence and pseudo-stability of finite-difference equations for an over-determined problem," Numer. Math., v. 4, 1962, pp. 277-292. MR 26 #5740. MR 0148232 (26:5740)
  • [10] R. D. Richtmyer, A Survey of Difierence Methods for Non-steady fluid Dynamics, N.C.A.R. Tech. Note 63-2, 1963.
  • [11] R. D. Richtmyer & K. W. Morton, Stability Studies for Finite Difference Equations, N.Y.U. Courant Inst. Math. Sci. Res. Dep. N.Y.O.-1480-5, 1964.
  • [12] S. Schechter, "Quasi-tridiagonal matrices and type-insensitive difference equations," Quart. Appl. Math., v. 18, 1960-61, pp. 258-295. MR 22 #5133. MR 0114309 (22:5133)
  • [13] W. G. Strang, "Accurate partial difference methods. II. Non-linear problems," Numer. Math., v. 6, 1964, pp. 37-46. MR 29 #4215. MR 0166942 (29:4215)
  • [14] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)

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DOI: https://doi.org/10.1090/S0025-5718-1968-0223114-8
Article copyright: © Copyright 1968 American Mathematical Society

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