I am looking at a paper by Ronald Smith 1999, (attached). The optimal weights he claims, obtains exact results for the Area, Centroid, Variance, Skewness and Kurtosis of solutions to the unforced advection-diffusion equation. Subsequently he arrives at the different parameters of the FD grid using some kind of moment matching which I do not understand how. I would appreciate some leads or directions to understanding this method.

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