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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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