Welcome to MODESpy

MODESpy implements generic methods for constructing and using parameterised linear multi-step methods to solve Ordinary Differential Equation Initial Value Problems (ODE IVPs). It is a Python implementation based on the MODES toolbox (Version 1.0.0) written in MATLAB from Lund University (see Authors below).

These methods are of variable step-size and order, and are regulated using digital control theory. MODESpy allows experimentation with different methods and regulation settings. Included is also a library of standard problems, which can be used to evaluate methods and settings.

MODESpy depends on SciPy and NumPy which should be installed before use.


The current version is 0.9.0. MODESpy is designed for Python >= 3.7 and is platform agnostic.


  • Python version 0.9.0 written by Eric J. Whitney, 2020.

  • Original MATLAB toolbox implementation by:
    • C. Arévalo - Center for Mathematical Sciences, Lund Institute of Technology, Lund, Sweden.

    • E Jonsson-Glans, J. Olander - HiQ Ace AB, Linköping, Sweden.

    • M. Selva-Soto - Department of Mathematical Engineering, University of Concepción, Chile.

    • G. Söderlind - Center for Mathematical Sciences, Lund University, Lund, Sweden.

The current version of the MATLAB toolbox is located at https://github.com/mss1972/MODES_v1.0


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