Ordinary differential equations

Thou, silent form, dost tease us out of thought / As doth eternity



Nothing here except a note about my favourite pragmatic intro to ODE analysis:

Homer Reid’s 18.305, Advanced Analytic Methods in Science and Engineering.

More to come, maybe. I might mention, say, the extensions to fractional DEs or stochastic DEs or partial differential equations or…

References

Alder, Michael. 2004. An Introduction to Complex Analysis for Engineers.
Arnold, V. I., and Richard A. Silverman. 1978. Ordinary Differential Equations. MIT Press.
Ascher, Uri M. 2008. Numerical methods for evolutionary differential equations. Computational science and engineering 5. Philadelphia, Pa: SIAM, Soc. for Industrial and Applied Mathematics.
Åström, Karl J, Richard M Murray, and EBL. 2008. Feedback systems: an introduction for scientists and engineers. Princeton: Princeton University Press. http://www.cds.caltech.edu/~murray/amwiki.
Borthwick, David. n.d. Introduction to Partial Differential Equations. Springer International Publishing.
Borzì, Alfio, and Volker Schulz. 2012. Computational Optimization of Systems Governed by Partial Differential Equations. Computational Science and Engineering Series. Philadelphia: Society for Industrial and Applied Mathematics.
Chen, Tian Qi, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. 2018. “Neural Ordinary Differential Equations.” In Advances in Neural Information Processing Systems 31, edited by S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, 6572–83. Curran Associates, Inc. http://papers.nips.cc/paper/7892-neural-ordinary-differential-equations.pdf.
Dandekar, Raj, Karen Chung, Vaibhav Dixit, Mohamed Tarek, Aslan Garcia-Valadez, Krishna Vishal Vemula, and Chris Rackauckas. 2021. “Bayesian Neural Ordinary Differential Equations.” arXiv:2012.07244 [cs], March. http://arxiv.org/abs/2012.07244.
Hairer, E., Christian Lubich, and Gerhard Wanner. 2010. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. 2nd ed. Springer Series in Computational Mathematics 31. Heidelberg ; New York: Springer.
Hairer, E., S. P. Nørsett, and Gerhard Wanner. 2009. Solving Ordinary Differential Equations I: Nonstiff Problems. 2nd rev. ed. Springer Series in Computational Mathematics 8. Heidelberg ; London: Springer.
Hairer, Ernst, Gerhard Wanner, and Ernst Hairer. 2010. Solving ordinary differential equations 2: Stiff and differential-algebraic problems. 2., rev. ed., corrected printing, 1. softcover printing. E. Hairer ; 2. Berlin: Springer.
Logg, Anders, Kent-Andre Mardal, Garth N. Wells, and others. 2012. Automated Solution of Differential Equations by the Finite Element Method. Springer. https://doi.org/10.1007/978-3-642-23099-8.
Lyons, Terry J., Michael Caruana, and Thierry Lévy. 2007. Differential Equations Driven by Rough Paths. Vol. 1908. Lecture Notes in Mathematics. Springer, Berlin. https://mathscinet.ams.org/mathscinet-getitem?mr=2314753.

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