An explicit stable numerical scheme for the 1D transport equation
Résumé
We derive in this paper a numerical scheme in order to calculate solutions of 1D transport equations. This 2nd-order scheme is based on the method of characteristics and consists of two steps: The first step is about the approximation of the foot of the characteristic curve whereas the second one deals with the computation of the solution at this point. The main idea in our scheme is to combine two 2nd-order interpolation schemes so as to preserve the maximum principle. The resulting method is unconditionaly stable and designed for classical solutions but turns out to remain valid when shocks occur.
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