CarlemanLinearization.jl

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This package implements the Carleman linearization transformation of polynomial differential equations in Julia.

Features

The following methods are available:

• Construction of the Carleman embedding using sparse matrices
• Explicit error bounds [FP17]
• Improved error bounds for dissipative systems [L20]

Related libraries

• carlin: Python library with similar functionality.
• CarlemanBurgers: MATLAB implementation of the classical Carleman solution of the viscous Burgers equation, used in https://arxiv.org/abs/2011.03185.

References

• [FP17] Forets, Marcelo, and Amaury Pouly. Explicit error bounds for carleman linearization. arXiv preprint arXiv:1711.02552 (2017).

• [L20] Liu JP, Kolden HØ, Krovi HK, Loureiro NF, Trivisa K, Childs AM. Efficient quantum algorithm for dissipative nonlinear differential equations. arXiv preprint arXiv:2011.03185. 2020 Nov 6.