Contributed Talk
Positive and conservative nonstandard schemes for biochemical systems
University of Bari Aldo Moro, Italy
Abstract
Many important phenomena in biology, chemistry, epidemiology and ecology are modelled by differential systems with two main qualitative characteristics: positive solutions and conservation of linear invariants, such as the total density. A suitable numerical integrator for these models should therefore be featured by the same two characteristics. In this work [1], we generalize the nonstandard Euler and Heun schemes in order to provide explicit geometric numerical integrators for biochemical systems, here denoted as GeCo schemes, which preserve both positivity of the solutions and linear invariants. We show the performance of GeCo schemes in solving some nonlinear biochemical systems and compare them with similar schemes in literature.
References
[1] Martiradonna, A., Colonna, G., Diele, F., GeCo: Geometric Conservative nonstandard schemes for biochemical systems. Applied Numerical Mathematics, 155, 38-57 (2020).
Joint work with Fasma Diele and Gianpiero Colonna, CNR, Italy