Implicit difference methods for nonlinear first order partial functional differential systems
Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 459-482
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type. Numerical examples are given.
DOI :
10.4064/am37-4-5
Keywords:
initial problems nonlinear hyperbolic functional differential systems considered classical solutions approximated solutions suitable quasilinear systems difference functional equations numerical methods difference schemes which implicit respect time variable theorems convergence difference schemes error estimates approximate solutions presented proof stability based comparison technique nonlinear estimates perron type numerical examples given
Affiliations des auteurs :
Elżbieta Puźniakowska-Gałuch 1
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author = {El\.zbieta Pu\'zniakowska-Ga{\l}uch},
title = {Implicit difference methods for nonlinear first order partial functional differential systems},
journal = {Applicationes Mathematicae},
pages = {459--482},
year = {2010},
volume = {37},
number = {4},
doi = {10.4064/am37-4-5},
zbl = {1219.35012},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am37-4-5/}
}
TY - JOUR AU - Elżbieta Puźniakowska-Gałuch TI - Implicit difference methods for nonlinear first order partial functional differential systems JO - Applicationes Mathematicae PY - 2010 SP - 459 EP - 482 VL - 37 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4064/am37-4-5/ DO - 10.4064/am37-4-5 LA - en ID - 10_4064_am37_4_5 ER -
%0 Journal Article %A Elżbieta Puźniakowska-Gałuch %T Implicit difference methods for nonlinear first order partial functional differential systems %J Applicationes Mathematicae %D 2010 %P 459-482 %V 37 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4064/am37-4-5/ %R 10.4064/am37-4-5 %G en %F 10_4064_am37_4_5
Elżbieta Puźniakowska-Gałuch. Implicit difference methods for nonlinear first order partial functional differential systems. Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 459-482. doi: 10.4064/am37-4-5
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