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math.NA2021★ 7 cited
Validated forward integration scheme for parabolic PDEs via Chebyshev series
Jacek Cyranka, Jean-Philippe Lessard
In this paper we introduce a new approach to compute rigorously solutions of Cauchy problems for a class of semi-linear parabolic partial differential equations. Expanding solution…
math.NA2018
Tight Continuous-Time Reachtubes for Lagrangian Reachability
Jacek Cyranka, Md. Ariful Islam, Scott A. Smolka +2
We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-var…