{'fraction_non_alphanumeric': 0.01741654571843251, 'fraction_numerical': 0.0, 'mean_word_length': 5.216216216216216, '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}}
Existence of non-spurious solutions to discrete boundary value problems

This paper investigates discrete boundary value problems (BVPs) involving secondorder difference equations and two-point boundary conditions. General theorems guaranteeing the existence and uniqueness of solutions to the discrete BVP are established. The methods involve a sufficient growth condition to yield an a priori bound on solutions to a certain family of discrete BVPs. The a priori bounds on solutions to the discrete BVP do not depend on the step-size and thus there are no “spurious” solutions. It is shown that solutions of the discrete BVP will converge to solutions of ordinary differential equations.