Opuscula Mathematica
Opuscula Math. 34, no. 2 (2014), 375-386

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
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Received: 2013-09-14.
Revised: 2013-11-02.
Accepted: 2013-11-07.
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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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