Thiele rational interpolation for the numerical computation of the reversible Randles-Sevcik function in electrochemistry (Q1566966)

The proposed method is the following one: To compute the function \(f(x)=\int_c^x K(x,y) dy\), the integral is evaluated (numerically) for a number of points and then rational interpolation is performed in these points. The function mentioned in the title is related because, up to a constant factor, it can be written as \(f(x)={d\over dx}\int_{-\infty}^x g(y)/(x-y)^{1/2} dy\), \(g(y)=1/(1+e^{-y})\). The Thiele algorithm is revised and several numerical examples are presented. To get interpolants that have an almost equi-oscillating error curve, the interpolation points are chosen like Chebyshev or contracted Chebyshev points in the interval of interest.