{'fraction_non_alphanumeric': 0.016227180527383367, 'fraction_numerical': 0.0, 'mean_word_length': 6.373134328358209, '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}}
Collocation‐variation difference schemes for differential‐algebraic equations

We consider the initial value problem in linear differential‐algebraic equations and highlight the difficulties of the construction of numerical methods for these problems. We propose one‐step difference schemes based on the collocation‐variational approach and show the principal difference between these algorithms and the known difference schemes. The analysis of the particular cases of such schemes are given.