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Paper IPM / M / 12420  


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, CrankNicolson and PredictorCorrector 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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