Opuscula Math. 34, no. 2 (2014), 375-386
http://dx.doi.org/10.7494/OpMath.2014.34.2.375

 
Opuscula Mathematica

Stability of finite difference schemes for generalized von Foerster equations with renewal

Henryk Leszczyński
Piotr Zwierkowski

Abstract. We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to \(l^1\) and \(l^\infty\) norms.

Keywords: structured model, renewal, finite differences, stability.

Mathematics Subject Classification: 65M06, 65M12, 92D25.

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  • Henryk Leszczyński
  • University of Gdansk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdansk, Poland
  • Piotr Zwierkowski
  • University of Gdansk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdansk, Poland
  • Received: 2013-09-14.
  • Revised: 2013-11-02.
  • Accepted: 2013-11-07.
Opuscula Mathematica - cover

Cite this article as:
Henryk Leszczyński, Piotr Zwierkowski, Stability of finite difference schemes for generalized von Foerster equations with renewal, Opuscula Math. 34, no. 2 (2014), 375-386, http://dx.doi.org/10.7494/OpMath.2014.34.2.375

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