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Numerical solution of the one phase 1D fractional Stefan problem using the front fixing method
Author(s) -
Błasik Marek,
Klimek Małgorzata
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.3292
Subject(s) - mathematics , stefan problem , front (military) , fractional calculus , derivative (finance) , scheme (mathematics) , numerical analysis , phase (matter) , space (punctuation) , mathematical analysis , computer science , physics , operating system , boundary (topology) , quantum mechanics , meteorology , financial economics , economics
In this paper, we present a novel numerical scheme to solve a 1D, one‐phase extended Stefan problem with fractional Caputo derivative with respect to time. The proposed method is based on a suitable choice of the new space coordinate for the subdiffusion equation and extends the front‐fixing method to the subdiffusion case. In the final part, examples of numerical results are discussed. Copyright © 2014 John Wiley & Sons, Ltd.