9 citations · 39 across the 26 of their papers we have counts for
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math.NA2021★ 4 cited
Microscopic Patterns in the 2D Phase-Field-Crystal Model
Gabriel Martine-La Boissoniere, Rustum Choksi, Jean-Philippe Lessard
Using the recently developed theory of rigorously validated numerics, we address the Phase-Field-Crystal (PFC) model at the microscopic (atomistic) level. We show the existence of…
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…