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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References | Similar Articles | Additional Information

**[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