Generalized method of lines for first order partial functional differential equations

• Autorzy: W. Czernous
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35R10: Partial functional-differential equations
• 65M20: Method of lines

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2006
• Tom: 89
• Numer: 2
• Strony: 103-126

Daty

wydano

2006

Twórcy

autor

W. Czernous

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

Identyfikatory

DOI

10.4064/ap89-2-1