{'fraction_non_alphanumeric': 0.01361573373676248, 'fraction_numerical': 0.0, 'mean_word_length': 5.490196078431373, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Time-domain simulation for fractional relaxation of Havriliak-Negami type

The time-simulation of models described by the Havriliak-Negami response function is a challenging problem due to the absence of an explicit formulation for the corresponding differential operator in the time-domain. In this work, we discuss a convolution quadrature rule with convolution weights evaluated on the basis of the representation of the response function in the Laplace transform domain. We describe a general and straightforward technique for the computation of the weights and we present some numerical experiments to illustrate the effectiveness of the proposed approach.