RATIONAL APPROXIMATION IN THE SENSE OF KATO FOR TRANSPORT SEMIGROUPS

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

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