Geodesic
Implicit difference methods for nonlinear first order partial functional differential systems
Elżbieta Puźniakowska-Gałuch1
1 Institute of Mathematics University of Gdańsk Wit Stwosz St. 57 80-952 Gdańsk, Poland
Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 459-482.

Voir la notice de l'article provenant de 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

Elżbieta Puźniakowska-Gałuch 1

1 Institute of Mathematics University of Gdańsk Wit Stwosz St. 57 80-952 Gdańsk, Poland 
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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. http://geodesic.mathdoc.fr/articles/10.4064/am37-4-5/

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