Approximate Solutions of Linearized Delay Differential Equations Arising from a Microbial Fermentation Process Using the Matrix Lambert Function
| Autor: | Kuntjoro Adji Sidarto, Agus Gunawan, Kasbawati Kasbawati |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
General Mathematics General Physics and Astronomy 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences General Biochemistry Genetics and Molecular Biology linearized delay differential system symbols.namesake Matrix (mathematics) 020901 industrial engineering & automation Control theory Lambert W function Applied mathematics 0101 mathematics Linear combination lcsh:Science lcsh:Science (General) Principal branch Mathematics Multidisciplinary microbial fermentation process Mode (statistics) General Chemistry General Medicine Delay differential equation Cuckoo Search algorithm Term (time) Zeroth law of thermodynamics symbols General Earth and Planetary Sciences lcsh:Q General Agricultural and Biological Sciences the Lambert function the zeroth mode lcsh:Q1-390 |
| Zdroj: | Journal of Mathematical and Fundamental Sciences, Vol 48, Iss 1, Pp 25-38 (2016) |
| ISSN: | 2338-5510 2337-5760 |
| Popis: | In this paper we present approximate solutions of linearized delay differential equations using the matrix Lambert function. The equations arise from a microbial fermentation process in a metabolic system. The delay term appears due to the existence of a rate-limiting step in the fermentation pathway. We find that approximate solutions can be written as a linear combination of the Lambert function solutions in all branches. Simulations are presented for three cases of the ratio of the rate of glucose supply to the maximum reaction rate of the enzyme that experienced delay. The simulations are worked out by taking the principal branch of the matrix Lambert function as the most dominant mode. Our present numerical results show that the zeroth mode approach is quite reliable compared to the results given by classical numerical simulations using the Runge-Kutta method. |
| Databáze: | OpenAIRE |
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