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

Leszczyński H., Zwierkowski P.

Opuscula Mathematica

2014

Vol. 34, no. 2

375--386

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 l1 and l∞ norms.

Convergence of a finite difference scheme for von Foerster equation with functional dependence

Zwierkowski P.

Demonstratio Mathematica

2012

Vol. 45, nr 3

725-737

We analyse a finite difference scheme for von Foerster-McKendrick type equations with functional dependence forward in time and backward with respect to one dimensional spatial variable. Some properties of solutions of a scheme are given. Convergence of a finite difference scheme is proved. The presented theory is illustrated by a numerical example.

Stability of forward-backward finite difference schemes for certain problems in biology

Zwierkowski P.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 2

181--203

We presemt a discretization method for a generalized von Foerster-type equation in many spatial variables. Stability of finite difference schemes on regular meshes is studied. If characteristic curves are decreasing, there are forward difference quotients applied. Otherwise, the derivatives are replaced by backward difference quotients.

Stability of forward finite difference schemes for certain problems in biology

Zwierkowski P.

Opuscula Mathematica

2003

Vol. 23

117-124

The subject of our considerations is a generalized von Foerster equation in many spatial variables. We present a discretization method of the initial value problem and study stability of finite difference schemes on regular meshes.