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The validity of the modified equation for nonlinear shock waves. (English) Zbl 0581.76072
The modified (model, equivalent) equation is an important tool in designing and analyzing nonlinear difference schemes. In this note, the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
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[1] Boris, J.; Book, D., J. comput. phys., 11, 38-69, (1973)
[2] Caflisch, R., Comm. pure appl. math., 32, 531-548, (1979)
[3] Chin, R., J. comput. phys., 18, 233-247, (1975)
[4] Engquist, B.; Osher, S., Math. comp., 34, 45-75, (1980)
[5] Feller, W., ()
[6] Harten, A., Comm. pure appl. math., 30, 611-638, (1977)
[7] {\scA. Harten}, High resolution schemes for hyperbolic conservation laws, to appear. · Zbl 0565.65050
[8] Harten, A.; Hyman, J.; Lax, P.D., Comm. pure appl. math., 29, 297-322, (1976)
[9] Hedstrom, G., Math. comp., 29, 969-977, (1975)
[10] Hirt, C., J. comput. phys., 2, 339-355, (1968)
[11] Illin, A.M.; Oleinik, O.A., Math. sb., 51, 191-232, (1960)
[12] Jennings, G., Comm. pure appl. math., 26, 25-37, (1973)
[13] Lax, P.D., Comm. pure appl. math., 10, 537-566, (1957)
[14] Lax, P.D., Accuracy and resolution in the computation of solutions of linear and nonlinear equations, (), 107-117
[15] Lerat, A., Numerical shock structure and nonlinear corrections for difference schemes in conservation form, (), 345-351
[16] Lerat, A.; Peyret, R., C. R. acad. sci. Paris ser. A, 276, 759-762, (1973)
[17] Majda, A.; Osher, S., Numer. math., 30, 429-452, (1978)
[18] Majda, A.; Ralston, J., Comm. pure appl. math., 32, 445-482, (1979)
[19] {\scD. Michelson}, Discrete shocks for difference approximations to systems of conservation laws, to appear. · Zbl 0627.76075
[20] Osher, S.; Ralston, J., Comm. pure appl. math., 35, 737-749, (1982)
[21] Warming, R.; Hyett, B., J. comput. phys., 14, 159-179, (1974)
[22] Zwas, G.; Roseman, J., J. comput. phys., 12, 179-186, (1973)
[23] Lax, P.D., On difference schemes for solving initial value problems for conservation laws, () · Zbl 0057.32502
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