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Enhanced Accuracy and Applicability of Analytico‐Numerical Solutions to Ordinary Differential Problems
Author(s) -
Reali M,
Dassie G
Publication year - 1991
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19910710717
Subject(s) - discretization , ordinary differential equation , bubble , numerical analysis , péclet number , mathematics , series (stratigraphy) , differential (mechanical device) , diffusion , computer science , differential equation , mechanics , mathematical analysis , physics , geology , thermodynamics , paleontology
Abstract This report concerns the potential of analytico‐numerical techniques based on Taylor series developments for solving classes of ordinary differential problems presenting remarkable numerical difficulties. Such techniques which are rather flexible and easily programmable may lead to very accurate solutions as is demonstrated with two problems which are worked out in detail. The first problem models a strongly non‐linear event, an underwater explosion leading to spherical bubble oscillations characterized by ultrarapid variations of the bubble/water interface velocity. The second problem, a steady‐state convective‐diffusion calculation, is also solved in a very accurate way even for very large Peclet numbers when solutions obtained form specific discretization techniques are much less accurate.