Generalized method of lines for first order partial functional differential equations

Tom 89 / 2006

W. Czernous Annales Polonici Mathematici 89 (2006), 103-126 MSC: 35R10, 65M20. DOI: 10.4064/ap89-2-1


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.


  • W. CzernousInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz St. 57
    80-952 Gdańsk, Poland

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek