Opuscula Mathematica

Opuscula Math.
 25
, no. 1
 (), 109-130
Opuscula Mathematica

Numerical approximations of difference functional equations and applications


Abstract. We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Keywords: functional differential equations, stability and convergence, interpolating operators, nonlinear estimates of the Perron type.
Mathematics Subject Classification: 35R10, 65M12.
Cite this article as:
Zdzisław Kamont, Numerical approximations of difference functional equations and applications, Opuscula Math. 25, no. 1 (2005), 109-130
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.