Notes on the stability of a non-linear scheme for calculating the motion of a shock wave
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1199-1204
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Using generally accepted methods of linearizing non-linear equations with subsequent local stability analysis, it is shown that a difference scheme for calculating the shift of a shock wave region, presented in a certain paper relating to the Godunov method, is unstable if considered in isolation. A simple scheme which has no such drawback is discussed here, and the problem of extending the algorithm to more variables is analyzed.
@article{ZVMMF_1983_23_5_a15,
author = {Yu. Ya. Mikhailov},
title = {Notes on the stability of a non-linear scheme for calculating the motion of a shock wave},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1199--1204},
publisher = {mathdoc},
volume = {23},
number = {5},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a15/}
}
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%0 Journal Article %A Yu. Ya. Mikhailov %T Notes on the stability of a non-linear scheme for calculating the motion of a shock wave %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1983 %P 1199-1204 %V 23 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a15/ %G ru %F ZVMMF_1983_23_5_a15
Yu. Ya. Mikhailov. Notes on the stability of a non-linear scheme for calculating the motion of a shock wave. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1199-1204. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a15/