Numerical solution of one-phase Stefan problem for the non-classical heat equation with a convective condition

Document Type : Research Paper

Authors

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

Abstract

A numerical technique for the solution of the one-phase Stefan problem for the non-classical heat equation with a convective condition is discussed. This approach is based on a scheme introduced in [16]. The compatibility and convergence of the method is proven. Numerical examples round out the discussion.

Keywords

References

  • [1] O. A. Arqub and B. Maayah, Adaptive the Dirichlet model of mobile/immobile advection/dispersion in a time- fractional sense with the reproducing kernel computational approach: Formulations and approximations, Internat. J. Modern Phys., (2022), 2350179.
  • [2] O. A. Arqub, H. Alsulami, and M. Alhodaly, Numerical Hilbert space solution of fractional Sobolev equation in (1+1)-dimensional space. Mathematical Sciences, Mathematical Sciences, (2022), 1-12.
  • [3] O. A. Arqub,The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations, Math. Meth. in the Appl. Sciences.37 (2016), 4549-4562.
  • [4] B. Babayar-Razlighi, K. Ivaz, and M.R. Mokhtarzadeh, Newton-Product Integration for a Stefan Problem with Kinetics, J. Sci. I. R. of Iran, 22 (2011), 51–61.
  • [5] B. Babayar-Razlighi, K. Ivaz, M. R. Mokhtarzadeh, and A. N. Badamchizadeh, Newton-product integration for a two-phase Stefan problem with kinetics, Bulletin of the Iranian Mathematical Society, 38 (2012), 853-868.
  • [6] H. Badawi, O. A. Arqub, and N. Shawagheh, Well-posedness and numerical simulations employing Legendre- shifted spectral approach for Caputo–Fabrizio fractional stochastic integrodifferential equations, Internat. J. Mod- ern Phys. B ,34 (2023), 2350070.
  • [7] S. Banei and K. Shanazari , Solving the forward-backward heat equation with a non-overlapping domain decompo- sition method based on multiquadric RBF meshfree method, Computational Methods for Differential Equations, 9 (2021), 1083-1099.
  • [8] A. C. Briozzo and D. A. Tarzia, A Stefan problem for a non-classical heat equation with a convective condition, Applied Mathematics and Computation, 217 (2010), 4051-4060.
  • [9] J. R. Cannon and M. Primicerio, Remarks on the one-phase Stefan problem for the heat equation with the flux prescribed on the fixed boundary, Journal of Mathematical Analysis and Applications, 35 (1971), 361-373.
  • [10] J. Crank,Free and moving boundary problems, Oxford, Clarendon press, (1984).
  • [11] M. Dehghan and S. Karimi Jafarbigloom, A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems, Computational Methods for Differential Equations, 9 (2021), 410-426.
  • [12] K. Ivaz and A. Beiranvand, Solving The Stefan Problem with Kinetics,Computational Methods for Differential Equations, 2 (2014), 37-49.
  • [13] K. Ivaz, M. Asadpour Fazlallahi, A. Khastan, and J. J. Nieto, Fuzzy one-phase Stefan problem, Appl. Comput. Math., 22 (2023), 66-79.
  • [14] K. Ivaz, Uniqueness of Solution for a Class of Stefan Problems, J. Sci. I. R. Iran, 13 (2002), 71-74.
  • [15] S. Kutluay, A. R. Bahadir, and A. Ozdes, The numerical solution of one-phase classical Stefan problem, Journal of computational and applied mathematics, 81 (1997), 135-144.
  • [16] A. Vasilios, Mathematical modeling of melting and freezing processes, Routledge, 2017.
Computational Methods for Differential Equations
Volume 11, Issue 4
July 2023
Pages 776-784

Files

History

  • Receive Date: 19 November 2022
  • Revise Date: 17 May 2023
  • Accept Date: 17 May 2023

Share

How to cite

Statistics