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math.NA2014
Godunov scheme for Maxwell's equations with Kerr nonlinearity
Denise Aregba-Driollet
We study the Godunov scheme for a nonlinear Maxwell model arising in nonlinear optics, the Kerr model. This is a hyperbolic system of conservation laws with some eigenvalues of var…
math.NA2012
Time Asymptotic High Order Schemes for Dissipative BGK Hyperbolic Systems
Denise Aregba-Driollet, Maya Briani, Roberto Natalini
We introduce a new class of finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using precise analytical time-…