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

100%

Zwierkowski P.

Commentationes Mathematicae

2005

tom 45

nr 2

We present 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.

Existence of solutions to generalized von Foerster equations with functional dependence

63%

Leszczyński H. , Zwierkowski P.

nr 3

201-210

We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).