On certain finite difference schemes for hyperbolic systems

Author:
John Gary

Journal:
Math. Comp. **18** (1964), 1-18

MSC:
Primary 65.67

DOI:
https://doi.org/10.1090/S0025-5718-1964-0158553-3

MathSciNet review:
0158553

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**[1]**R. Courant & K. O. Friedrichs,*Supersonic Flow and Shock Waves*, Interscience Publishers, New York, 1948, p. 95. MR**0029615 (10:637c)****[2]**G. E. Forsythe & W. R. Wasow,*Finite Difference Methods for Partial Equations*, John Wiley and Sons, New York, 1960, p. 237. MR**0130124 (23:B3156)****[3]**P. D. Lax & B. Wendroff,*Difference Schemes with High Order of Accuracy for Solving Hyperbolic Systems*, Report NYO-9759, A.E.C. Computing and Applied Math. Center, New York University, 1962.**[4]**R. D. Richtmyer,*Difference Methods for Initial Value Problems*, Interscience Publishers, New York, 1957. MR**0093918 (20:438)****[5]**S. Schechter, ``Quasi-tridiagonal matrices and type-insensitive difference equations,''*Quart. Applied Math.*, v. 18, 1960, p. 285-295. MR**0114309 (22:5133)****[6]**P. D. Lax & B. Wendroff, ``Systems of conservation laws,''*Comm. Pure Appl. Math.*, v. 13, 1960, p. 217-237. MR**0120774 (22:11523)****[7]**P. D. Lax, ``Weak solutions of nonlinear hyperbolic equations and their numerical solution,''*Comm. Pure Appl. Math.*, 7, 1954, p. 159. MR**0066040 (16:524g)****[8]**L. Filler & H. Ludloff, ``Stability analysis and integration of the viscous equations of motion,''*Math. Comp.*, v. 15, 1961, p. 261-274. MR**0129556 (23:B2592)****[9]**S. Burstein, to appear as NYO Report, A. E. C. Computing and Applied Math. Center, New York University. MR**522091 (80b:76001)****[10]**J. Douglas & B. F. Jones, ``On predictor-corrector methods for non-linear parabolic differential equations,''*SIAM Jour.*, v. 11, 1963, p. 195-204. MR**0153123 (27:3092)**

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DOI:
https://doi.org/10.1090/S0025-5718-1964-0158553-3

Article copyright:
© Copyright 1964
American Mathematical Society