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A comprehensive comparison of ODE solvers for biochemical problems

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  • Postawa, Karol
  • Szczygieł, Jerzy
  • Kułażyński, Marek

Abstract

The article is focused on a deep and detailed study on available Ordinary Differential Equations (ODEs) numerical solvers for biochemical and bioprocesses purposes, which are an important part of the renewable energy sector. A wide selection of algorithms is tested - starting from simple, single-step explicit methods, ending with implicit multi-step techniques. These include MATLAB, Python, C++, and C# implementations. The test configuration is an ODEs based model that simulates a biogas production reactor. The research shows that most of the tested solvers pass the accuracy-test (the difference didn’t exceed 0,07%), however only selected are efficient. Most of Runge-Kutta based methods are slow and require an enormous number of steps (more than 2.5 × 108). Only multi-step implicit methods are long term solutions - they provide great accuracy while dealing well with stiff, non-smooth ODEs sets. The best from tested solutions were two MATLAB solvers - ode23s and ode15s, as well as a python solver - the LSODA. The first needed averagely 84,051s of calculation time, and 96465 steps, while ode15s required just 11,529s, performing over 20-times fewer steps. The LSODA is ranked somewhere between them with 18,806s of calculation time and the total number of 23730 steps for tested ODEs set.

Suggested Citation

  • Postawa, Karol & Szczygieł, Jerzy & Kułażyński, Marek, 2020. "A comprehensive comparison of ODE solvers for biochemical problems," Renewable Energy, Elsevier, vol. 156(C), pages 624-633.
    • Handle: RePEc:eee:renene:v:156:y:2020:i:c:p:624-633
    DOI: 10.1016/j.renene.2020.04.089
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