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Efficient numerical schemes for solving the self‐consistent field equations of flexible–semiflexible diblock copolymers
Author(s) -
Liang Qin,
Jiang Kai,
Zhang Pingwen
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2868
Subject(s) - gradient descent , conjugate gradient method , robustness (evolution) , mathematics , position (finance) , descent (aeronautics) , method of steepest descent , field (mathematics) , scheme (mathematics) , mathematical optimization , mathematical analysis , computer science , physics , pure mathematics , artificial neural network , biochemistry , chemistry , finance , machine learning , meteorology , economics , gene
We present two efficient iterative schemes for solving the self‐consistent field equations of flexible–semiflexible diblock copolymers. One is a semi‐implicit scheme developed by employing asymptotic expansion, and the other is a hybrid scheme combining the robustness of the steepest descent method with the efficiency of the conjugate gradient method. In our position‐one‐dimensional and position‐two‐dimensional numerical experiments, we demonstrate that these schemes are much more efficient than the steepest descent method. Copyright © 2013 John Wiley & Sons, Ltd.