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Paper   IPM / M / 12420
School of Mathematics
  Title:   Rational approximation in the sense of Kato for transport semigroups
  Author(s):  H. Emamirad (Joint with M. A. Cherif and M. Mnif)
  Status:   Published
  Journal: Int. J. Finite Vol.
  Vol.:  8
  Year:  2012
  Pages:   1-23
  Supported by:  IPM
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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