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]**John Gary,*On certain finite difference schemes for hyperbolic systems*, Math. Comp.**18**(1964), 1–18. MR**0158553**, https://doi.org/10.1090/S0025-5718-1964-0158553-3**[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]**Peter Lax and Burton Wendroff,*Systems of conservation laws*, Comm. Pure Appl. Math.**13**(1960), 217–237. MR**0120774**, https://doi.org/10.1002/cpa.3160130205**[7]**Peter D. Lax and Burton Wendroff,*Difference schemes for hyperbolic equations with high order of accuracy*, Comm. Pure Appl. Math.**17**(1964), 381–398. MR**0170484**, https://doi.org/10.1002/cpa.3160170311**[8]**P. D. Lax and R. D. Richtmyer,*Survey of the stability of linear finite difference equations*, Comm. Pure Appl. Math.**9**(1956), 267–293. MR**0079204**, https://doi.org/10.1002/cpa.3160090206**[9]**Seymour V. Parter,*Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem*, Numer. Math.**4**(1962), 277–292. MR**0148232**, https://doi.org/10.1007/BF01386319**[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]**Samuel Schechter,*Quasi-tridiagonal matrices and type-insensitive difference equations.*, Quart. Appl. Math.**18**(1960/1961), 285–295. MR**0114309**, https://doi.org/10.1090/S0033-569X-1960-0114309-X**[13]**Gilbert Strang,*Accurate partial difference methods. II. Non-linear problems*, Numer. Math.**6**(1964), 37–46. MR**0166942**, https://doi.org/10.1007/BF01386051**[14]**Richard S. Varga,*Matrix iterative analysis*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR**0158502**

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0223114-8

Article copyright:
© Copyright 1968
American Mathematical Society