Numerical scheme for one phase 1D fractional Stefan problem using the similarity variable technique

• Autorzy: Błasik M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a numerical method to solve a one-dimensional, one-phase extended Stefan problem with fractional time derivative described in the Caputo sense. The proposed method is based on applying a similarity variable for the anomalous-diffusion equation and the finite difference method. In the final part, examples of numerical results are discussed.

Słowa kluczowe

EN

Stefan problem; anomalous diffusion; fractional derivative; finite difference method

PL

zagadnienie Stefana; dyfuzja anomalna; pochodna ułamkowa; metoda różnic skończonych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 1
• Strony: 13--21
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Błasik M.

• Institute of Mathematics, Czestochowa University of Technology, Częstochowa, Poland

Bibliografia

• [1] Aoki Y., Sen M., Paolucci S., Approximation of transient temperatures in complex geometries using fractional derivatives, Heat Mass Transfer 2008, 44, 771-777.
• [2] Voller V., An exact solution of a limit case Stefan problem governed by a fractional diffusion equation, International Journal of Heat and Mass Transfer 2010, 53, 5622-5625.
• [3] Liu Junyi, Xu Mingyu, An exact solution to the moving boundary problem with fractional anomalous diffusion in drug release devices, Zeitschrift für Angewandte Mathematik und Mechanik 2004, 84, 22-28.
• [4] Liu Junyi, Xu Mingyu, Some exact solutions to Stefan problems with fractional differential equations, Journal of Mathematical Analysis and Applications 2009, 351, 536-542.
• [5] Xicheng Li, Mingyu Xu, Xiaoyun Jiang, Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition, Applied Mathematics and Computation 2009, 208, 434-439.
• [6] Xicheng Li, Mingyu Xu, Shaowei Wang, Scale-invariant solutions to partial differential equations of fractional order with a moving boundary condition, Journal of Physics A: Mathematical and Theoretical 2008, 41, 155-202.
• [7] Li Xi-cheng, Fractional Moving Boundary Problems and Some of Its Applications to Controlled Release System of Drug, PhD thesis, Shandong University 2009.
• [8] Chen Yin, Xicheng Li, Anomalous diffusion of drug release from slab matrix: Fractional diffusion models, International Journal of Pharmaceutics 2011, 418, 78-87.
• [9] Błasik M., Klimek M., Numerical scheme for the one-phase 1D fractional Stefan problem, Proceedings of the 20th CMM 2013 International Conference on Computer Methods in Mechanics, Poznań, Poland, 27-31 August 2013.
• [10] Rajeev, Kushwaha M.S., Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation, Applied Mathematical Modelling 2013, 37, 3589-3599.