{'fraction_non_alphanumeric': 0.029490616621983913, 'fraction_numerical': 0.0, 'mean_word_length': 5.073170731707317, '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}}
State Analysis of Time-Varying Singular Bilinear Systems by RK-Butcher Algorithms

The Runge-Kutta (RK)-Butcher algorithm is used to study the timevarying singular bilinear systems with the exact solutions. The results (discrete solutions) obtained using the Haar wavelets, Single-Term Walsh series (STWS) and RK-Butcher algorithms are compared with the exact solutions of the time-varying singular bilinear systems. It is found that the solution obtained using the RK-Butcher algorithm is closer to the exact solutions of the time-varying singular bilinear systems. The RK-Butcher algorithm can easily be implemented using a digital computer and the solution can be obtained for any length of time, which is an added advantage of this algorithm.