Comparison of explicit and implicit difference schemes for parabolic functional differential equations

• Autorzy: Zdzisław Kamont , Karolina Kropielnicka
• Języki publikacji: EN

Abstrakty

EN

Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It is shown that the conditions on the mesh for explicit difference schemes are more restrictive than the suitable assumptions for implicit methods. There are implicit difference schemes which are convergent while the corresponding explicit difference methods are not convergent. Error estimates for both methods are constructed.

Kategorie tematyczne

• 35R10: Partial functional-differential equations
• 65M12: Stability and convergence of numerical methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 103
• Numer: 2
• Strony: 135-160

Daty

wydano

2012

Twórcy

autor

Zdzisław Kamont

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

autor

Karolina Kropielnicka

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

Identyfikatory

DOI

10.4064/ap103-2-3