Abstract
Based on a truncated Fourier series technique to compute stable derivatives in a Sobolev space setting, we propose a method for numerical differentiation of periodic functions from a finite amount of noisy data. In our method, we construct stable approximations to high order derivatives by filtering high frequency components of spectral derivatives obtained through the Fourier differentiation matrix. We derive convergence rates for the approximate derivatives with essentially the same accuracy as those obtained by the truncated Fourier series technique. Our method is illustrated with numerical examples, focusing in particular, on the estimation of the heat flux distribution in coiled tubes from experimental temperature data.
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