Numerical Tests of Center Series

Jorge L. deLyra

Department of Mathematical Physics, Physics Institute, University of São Paulo

April 3, 2015


We present numerical tests of several simple examples of center series, with the aim of evaluating the speed with which they converge, as compared to the corresponding Fourier series. These center series were defined and developed in previous papers, and constitute an improved form of trigonometric expansion of real functions, related to the Fourier series. The tests performed are comparative ones, between each Fourier series and the corresponding first-order center series. They show that, specially in the case of Fourier series that converge very slowly, the use of the center series can represent a truly enormous numerical and computational advantage. We also use the numerical advantage provided by the center series to display the Fourier Conjugate functions of each example worked out, as well as to test the speed of convergence of their Fourier series and first-order center series. For the execution of the comparative tests between the Fourier and first-order center series it was necessary, in some cases, to use also the second-order center series, as tools for the tests, since these converge even faster than the first-order center series.