Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous ¹   ; Z. Kamont ¹

¹ Institute of Mathematics University of Gdańsk Wit Stwosz St. 57 80-952 Gdańsk, Poland

Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 315-340

Résumé

We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit and implicit difference methods. We use a comparison technique with nonlinear estimates of Perron type for given functions with respect to the functional variables.

Détail

DOI : 10.4064/am38-3-4

Keywords: theorem error estimates approximate solutions explicit implicit difference functional equations unknown functions several variables apply general result investigate stability difference methods quasilinear functional differential equations initial boundary condition dirichlet type consider first order partial functional differential equations parabolic functional differential problems compare properties explicit implicit difference methods comparison technique nonlinear estimates perron type given functions respect functional variables