Geodesic
Generalized method of lines for first order partial functional differential equations
W. Czernous1
1 Institute of Mathematics University of Gdańsk Wit Stwosz St. 57 80-952 Gdańsk, Poland
Annales Polonici Mathematici, Tome 89 (2006) no. 2, pp. 103-126.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization in time of the method of lines considered in this paper leads to new difference schemes for the original problem. It is shown by examples that the new method is considerably better than the classical schemes.
DOI : 10.4064/ap89-2-1
Keywords: classical solutions initial boundary value problems approximated solutions associated differential difference problems method lines unknown function original problem its partial derivatives respect spatial variables constructed complete convergence analysis method given stability result proved using differential inequalities nonlinear estimates perron type given operators discretization time method lines considered paper leads difference schemes original problem shown examples method considerably better classical schemes

W. Czernous 1

1 Institute of Mathematics University of Gdańsk Wit Stwosz St. 57 80-952 Gdańsk, Poland 
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 partial functional differential equations
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 partial functional differential equations
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W. Czernous. Generalized method of lines for first order
 partial functional differential equations. Annales Polonici Mathematici, Tome 89 (2006) no. 2, pp. 103-126. doi : 10.4064/ap89-2-1. http://geodesic.mathdoc.fr/articles/10.4064/ap89-2-1/

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