@inproceedings{ale-wan-18-aa-reach,
  author = {Alexandre dit Sandretto, Julien and Wan, Jian},
  title = {Reachability Analysis of Nonlinear {ODEs} using Polytopic Based Validated {Runge}-{Kutta}},
  booktitle = {Proceedings of the 2018 International Conference on Reachability Problems (RP)},
  year = 2018,
  month = aug,
  series = {Lecture Notes in Computer Science},
  volume = {11123},
  pages = {1–14},
  doi = {10.1007/978-3-030-00250-3_1},
  comment = {Validated Runge-Kutta. Calls AA zonotopic computation. Replaces by general polytopes?}
  abstract = {Ordinary Differential Equations (ODEs) are a general form of differential equations. This mathematical format is often used to represent the dynamic behavior of physical systems such as control systems and chemical processes. Linear ODEs can usually be solved analytically while nonlinear ODEs may need numerical methods to obtain approximate solutions. There are also various developments for validated simulation of nonlinear ODEs such as explicit and implicit guaranteed Runge-Kutta integration schemes. The implicit ones are mainly based on zonotopic computations using affine arithmetics. It allows to compute the reachability of a nonlinear ODE with a zonotopic set as its initial value. In this paper, we propose a new validated approach to solve nonlinear ODEs with a polytopic set as the initial value using an indirectly implemented polytopic set computation technique.} 
}