MATLAB toolbox for structural preprocessing of differential-algebraic equations (DAEs).
In solving high-index DAEs using ode15i, index reduction is important preprocessing prior to numerical integration.
The Mattsson–Söderlind index reduction method (MS-method), which is implemented as reduceDAEIndex in MATLAB, is effective and commonly used; however, it is known to fail for some DAEs.
This toolbox provides a preprocessing function that modifies a given DAE system to an equivalent system that can be handled by the MS-method.
- MATLAB R2020b
- Symbolic Math Toolbox™
See doc/demo.md and doc/document.md.
Download and add src directory to the search path in MATLAB as follows:
- Windows:
addpath('c:\path\to\DAEPreprocessingToolbox\src')- Mac, Linux:
addpath('/path/to/DAEPreprocessingToolbox/src')See MATLAB addpath help page and MATLAB help page for adding a search path at startup.
Taihei Oki (University of Tokyo)
- Substituion and augmentation methods: https://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/drab094/6470741
- Mixed matrix method: https://dl.acm.org/doi/10.1145/3341499
Cite as:
T. Oki. Improved structural methods for nonlinear differential-algebraic equations via combinatorial relaxation. IMA Journal of Numerical Analysis, 43(1):357–386, 2023.
S. Iwata, T. Oki, and M. Takamatsu. Index reduction for differential-algebraic equations with mixed matrices. Journal of the ACM, 66(5), 2019.
This project is supported by JST CREST “Developing Optimal Modeling Methods for Large-Scale Complex Systems” Team and by JST ACT-I JST ACT-I “Information and Future”.