Stability of finite difference schemes for hyperbolic initial boundary value problems II
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 1, p. 37-98

We study the stability of finite difference schemes for hyperbolic initial boundary value problems in one space dimension. Assuming 2 -stability for the discretization of the hyperbolic operator as well as a geometric regularity condition, we show that the uniform Kreiss-Lopatinskii condition yields strong stability for the discretized initial boundary value problem. The present work extends the results of [4,7] to the widest possible class of finite difference schemes by dropping the technical assumptions of our former work [4]. We give some new examples of numerical schemes for which our results apply.

Published online : 2018-06-21
Classification:  65M12,  65M06,  35L50
@article{ASNSP_2011_5_10_1_37_0,
     author = {Coulombel, Jean-Fran\c cois},
     title = {Stability of finite difference schemes for hyperbolic initial boundary value problems II},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {1},
     year = {2011},
     pages = {37-98},
     zbl = {1225.65089},
     mrnumber = {2829318},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2011_5_10_1_37_0}
}
Coulombel, Jean-François. Stability of finite difference schemes for hyperbolic initial boundary value problems II. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 1, pp. 37-98. http://www.numdam.org/item/ASNSP_2011_5_10_1_37_0/

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