RATIONAL APPROXIMATION IN THE SENSE OF KATO FOR TRANSPORT SEMIGROUPS

Mohamed Amine Cherif † (1) , Hassan Emamirad (2) , Maher Mnif (1)

1 I.P.E.I.S
2 UP - Université de Poitiers = University of Poitiers

In this paper we mix the rational approximation procedure, which is a time approximation with approximation in the sense of Kato, which is a space approximation for linear transport equation. In 1970, H. J. Hejtmanek gave such a procedure for approximation of the linear transport equation and he proved the convergence only for explicit Euler scheme. We extend this procedure to explicit and implicit Euler, Crank-Nicolson and Predictor-Corrector schemes which have the rate 1,2 and 3 in the sense of rational approximation. Finally, we construct the numerical illustration for justifying the above rate of convergence.

Mots clés: rational function; absorption; production transport semigroups

Domaines: Equations aux dérivées partielles [math.AP]

Mohamed Amine Cherif †, Hassan Emamirad, Maher Mnif. RATIONAL APPROXIMATION IN THE SENSE OF KATO FOR TRANSPORT SEMIGROUPS . International Journal on Finite Volumes, 2012, 8, pp.1-23. ⟨hal-01121332⟩