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DRE-RKSM-REAL
A MATLAB implementation of order reduction onto the rational Krylov subspace for solving the differential Riccati equation can be downloaded here or here.
Related Article:
Kirsten, G., & Simoncini, V. (2019). Order reduction methods for solving large-scale differential matrix Riccati equations. SIAM J. Scient. Computing, v. 42 (4), 2020, pp. A2182-A2205. DOI: 10.1137/19M1264217.
2S-POD-DEIM for semilinear matrix ODEs
A MATLAB implementation of the 2S-POD-DEIM algorithm to integrate a class of semilinear matrix ODEs, where the reduced model is integrated by a matrix-oriented first-order exponential Euler scheme can be downloaded here.
Related Article:
G. Kirsten and Valeria Simoncini. A matrix-oriented POD-DEIM algorithm applied to nonlinear differential matrix equations. pp. 1-25, June 2020. Revised May 2021. arXiv: 2006.13289 [math.NA].
HO-POD-DEIM for semilinear tensor ODEs
A MATLAB implementation of the HO-POD-DEIM algorithm to integrate a class of semilinear tensor ODEs, where the reduced model is integrated by a tensor 2-SBDF scheme can be downloaded here.
Related Article:
G. Kirsten. Multilinear POD-DEIM model reduction for 2D and 3D nonlinear systems of differential equations. pp. 1-25, March 2021. Revised July 2021. arXiv: 2103.04343 [math.NA]. To apper in J. Computational Dynamics.