Relative error ϵ in the first derivative of density ρ(x) = (1 + x) g cm-3 as a function of the smoothing length (in interparticle units) calculated using both tensor and standard SPH schemes. Crosses are for direct derivative estimation. Upper left is for the error when the Gaussian kernel is used. The upper right picture shows the contribution of several error sources to the total error ϵ. Bottom pictures are the same but for the cubic-spline kernel.
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