A simple NSFD inspired method for Monod kinetics with small half saturation constants in the chemostat setting
Hermann Eberl
AI summary
70% confidenceThe paper proposes a simple, low-order method inspired by Nonstandard Finite Difference schemes to solve Monod kinetics equations with small half-saturation constants in chemostat settings, where traditional solvers fail.
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Abstract
Monod kinetics is an important nonlinearity that appears in mathematical modelling of microbial systems, but (under different names) also in many other applications in Mathematical Biology and Process Engineering. Although seemingly innocuous, for some extreme parameter values (notably very small half saturation concentrations and large decay rates), sophisticated high order solvers for ordinary differential equations have been known to fail. We explore this breakdown situation and suggest a simple, low order, easy to implement method that is inspired by so-called Nonstandard Finite Difference or Mickens schemes. We find that these can be a viable alternative to modern initial value problem solvers, in the problematic cases of extreme parameter values.
Key findings
- The proposed method is effective in solving Monod kinetics equations with extreme parameter values.
- The method is easy to implement and requires low computational resources.
- The results show that the proposed method is a viable alternative to modern initial value problem solvers in the problematic cases of extreme parameter values.
Keywords
Identifiers
- Journal
- Contemporary Mathematics
- Year
- 2024