COPADS IV: Fixed Time-Step ODE Solvers for a System of Equations Implemented as a Set of Python Functions

Maurice HT Ling


Ordinary differential equation (ODE) systems are commonly used many different fields. The de-facto method to implement an ODE system in Python programming using SciPy requires the entire system to be implemented as a single function, which only allow for inline documentation. Although each equation can be broken up into sub-equations, there is no compart-mentalization of sub-equations to its ODE. A better method will be to implement each ODE as a function. This encapsulates the sub-equations to its ODE, and allow for function and inline documentation, resulting in better maintainability. This study presents the implementation 11 ODE solvers that enable each ODE in a system to be implemented as a function. Three enhancements will be added. Firstly, the solvers will be implemented as generators to allow for virtually infinite simulation and returning a stream of intermediate results for analysis. Secondly, the solvers will allow for non-ODE-bounded variables or solution vector to improve code and results documentation. Lastly, a means to set upper and lower boundary of ODE solutions will be added. Validation testing shows that the enhanced ODE solvers give comparable results to SciPy’s default ODE solver. The implemented solvers are incorporated into COPADS repository (


ODE solvers; system of ODEs; Python; Documentation; one-ODE-one-function

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