Local linearization method: Difference between revisions

Revision as of 17:18, 8 December 2020

Revision as of 17:21, 8 December 2020

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HOLL discretizations are, for instance, the followings:

* ''Locally Linearized Runge Kutta discretization''<ref name=":1">de la Cruz H.; Biscay R.J.; Carbonell F.; Jimenez J.C.; Ozaki T. (2006). "Local Linearization-Runge Kutta (LLRK) methods for solving ordinary differential equations". Lecture Note in Computer Sciences 3991: 132–139, Springer-Verlag. Lecture Notes in Computer Science. 3991: 132–139. [http://doi.org/10.1007%2F11758501_22 [doi:10.1007/11758501_22]]. {{ISBN|978-3-540-34379-0}}.</ref><ref name=":3">de la Cruz H.; Biscay R.J.; Jimenez J.C.; Carbonell F. (2013). "Local Linearization - Runge Kutta Methods: a class of A-stable explicit integrators for dynamical systems". Math. Comput. Modelling. 57 (3–4): 720–740. [http://doi.org/10.1016%2Fj.mcm.2012.08.011. doi:10.1016/j.mcm.2012.08.011.]</ref>

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<math>\qquad \mathbf{z}_{n+1}=\mathbf{z}_{n}+\mathbf{\phi }(t_{n},\mathbf{z}