COPADS VI Fixed Time Step ODE Solvers with Mixed ODE and non ODE Function, and Script Generator.

Citation: Ling, MHT. 2018. COPADS VI: Fixed Time-Step ODE Solvers with Mixed ODE and non-ODE Function, and Script Generator. In Current STEM, Volume 1, pp. 173-212. Nova Science Publishers, Inc. ISBN 978-1-53613-416-2.

Link to [PDF] in my archive.

Ordinary differential equations (ODEs) are commonly used in mathematical modelling. However, the standard means of implementing a system of ODEs in Python, using Scipy, does not allow for each ODE to be implemented as an individual Python function. This results in poor documentation and maintainability. We have re-implemented 11 fixed-steps ODE solvers to allow for an ODE system to be implemented as a set of Python functions. Here, the ODE solvers are enhanced to take on a non-ODE function, allowing for modification of the ODE result vector at each time step, which may be useful in cases where one or more results has to be calibrated using other results. In addition, a script generator is implemented to assist in the generation of a Python ODE script from a set of parameters. This module had been incorporated into the Collection of Python Algorithms and Data Structures (COPADS; https://github.com/mauriceling/copads), under Python Software Foundation License version 2.