An Iteration Method for the Determination of Relaxation Spectra

Abstract
The determination of relaxation spectra involves the numerical solution of certain linear, convolution-type integral equations of the first kind. A simple iteration method is shown by which some such equations may be solved. In the limit this is equivalent to the exact solution by means of Fourier integrals. If only moderate accuracy is required, the iteration method is sometimes less laborious than the use of Fourier series, proposed earlier, and in any case it involvees only elementary arithmetical operations. As one illustration, the relaxation spectrum of polyisobutylene is found from the damping, for the whole domain over which published data are available. In the rubber-glass transition region the results agree well with those previously obtained for this region by use of Fourier series. As a second illustration, successive approximations to a fictitious single line spectrum are shown.

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