Treffer: A comprehensive comparison of ODE solvers for biochemical problems.

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. • The mathematical modeling as support in the design of bioenergy generation. • A wide selection of ODE solvers is evaluated. • Implicit methods are the most efficient for bioprocess models. • Different calculation environment can be utilized – MATLAB, Python, C++, C#. [ABSTRACT FROM AUTHOR]

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