{'fraction_non_alphanumeric': 0.013435700575815739, 'fraction_numerical': 0.0, 'mean_word_length': 5.6075949367088604, '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}}
A Model Numerical Scheme for the Propagation of phase Transitions in Solids

In this paper, we devise a simple finite difference scheme that produces approximations to the viscosity-capillarity solutions of the equations that govern the propagation of phase transitions in solids (or to the equations of van der Waals fluids) for all positive values of the dimensionless parameter that characterizes the viscosity-capillarity solution. Numerical experiments showing the convergence properties of the method are presented.