%0 Journal Article %T Solution to an ice melting cylindrical problem %A Boureghda, Abdellatif %J Journal of Nonlinear Sciences and Applications %D 2016 %V 9 %N 4 %@ ISSN 2008-1901 %F Boureghda2016 %X We give a solution to an ice melting cylindrical problem using the ''modified variable time step method'', earlier suggested by the author. New numerical techniques are proposed for the one-dimensional melting problem. The numerical results are obtained for the position of the moving boundary, time and temperatures. %9 journal article %R 10.22436/jnsa.009.04.04 %U http://dx.doi.org/10.22436/jnsa.009.04.04 %P 1440--1452 %0 Journal Article %T A Galerkin method for Stefan problems %A N. S. Asaithambi %J Appl. Math. Comput. %D 1992 %V 52 %F Asaithambi1992 %0 Book %T Numerical methods for solving one dimensional problems with a moving boundary %A A. Boureghda %D 1988 %I M. Sc. thesis, Department of Computing Science, Glasgow University, Scotland %C United Kingdom %F Boureghda1988 %0 Journal Article %T Numerical solution of the oxygen diffusion in absorbing tissue with a moving boundary %A A. Boureghda %J Comm. Numer. Methods Engrg. %D 2006 %V 22 %F Boureghda2006 %0 Journal Article %T Numerical solution of the oxygen diffusion problem in cylindrically shaped sections of tissue %A A. Boureghda %J Internat. J. Numer. Methods Fluids %D 2008 %V 56 %F Boureghda2008 %0 Book %T Moving boundary value problems %A A. Boureghda %D 2008 %I Doctorat en Sciences Mathématiques (Ph.D thesis), between Department of Mathematics, Ferhat Abbas University, Sétif Algeria and LMIA Haute Alsace University, Mulhouse %C France %F Boureghda2008 %0 Journal Article %T A modified variable time step method for solving ice melting problem %A A. Boureghda %J J. Difference Equ. Appl. %D 2012 %V 18 %F Boureghda2012 %0 Journal Article %T Numerical methods for one-dimensional Stefan problems %A J. Caldwell %A Y. Y. Kwan %J Comm. Numer. Methods Engrg. %D 2004 %V 20 %F Caldwell2004 %0 Journal Article %T Starting solutions for the boundary immobilization method %A J. Caldwell %A Y. Y. Kwan %J Comm. Numer. Methods Engrg. %D 2005 %V 21 %F Caldwell2005 %0 Book %T Finite difference methods %A J. Crank %D 1974 %I in: Moving Boundary Problems in Heat Flow and Diffusion, ed. by J. R. Ockendon and R. Hodgkins, Clarendon Press %C Oxford %F Crank1974 %0 Book %T Free and moving boundary problems %A J. Crank %D 1984 %I Clarendon Press %C Oxford %F Crank1984 %0 Journal Article %T A uniqueness theorem for the solution of Stefan problem %A J. Douglas %J Proc. Amer. Math. Soc. %D 1957 %V 8 %F Douglas1957 %0 Journal Article %T A numerical solution of the Stefan problem with a Neumann type boundary condition by enthalpy method %A A. Esen %A S. Kutluay %J Appl. Math. Comput. %D 2004 %V 148 %F Esen2004 %0 Journal Article %T A note on the existence of a solution to a problem of Stefan %A G. W. Evans %J Quart. Appl. Math. %D 1951 %V 9 %F Evans1951 %0 Book %T What are the best numerical methods in Moving Boundary Problems in Heat Flow and Diffusion %A L. Fox %D 1975 %I Clarendon Press %C Oxford %F Fox1975 %0 Book %T A survey of the formulation and solution of free and moving boundary Stefan problems %A R. M. Furzeland %D 1977 %I Brunel University Technical Report %C London %F Furzeland 1977 %0 Journal Article %T A comparative study of numerical methods for moving boundary %A R. M. Furzeland %J J. Inst. Math. Appl. %D 1980 %V 26 %F Furzeland 1980 %0 Book %T One-dimensional Stefan problems: an introduction %A J. M. Hill %D 1987 %I John Wiley & Sons, Inc. %C New York %F Hill1987 %0 Book %T Fachbereich Mathematik %A K. H. Hoffmann %D 1977 %I Berlin Freie Univesitat %C Germany %F Hoffmann1977 %0 Journal Article %T A comparison of numerical models for one-dimensional Stefan problems %A E. Javierre %A C. Vuik %A F. J. Vermolen %A S. Van der Zwaag %J J. Comput. Appl. Math. %D 2006 %V 192 %F Javierre2006 %0 Journal Article %T Numerical schemes for one-dimensional Stefan-like problems with a forcing term %A S. Kutluay %J Appl. Math. Comput. %D 2005 %V 168 %F Kutluay 2005 %0 Journal Article %T An isotherm migration formulation for one-phase Stefan problem with a time dependent Neumann condition %A S. Kutluay %A A. Esen %J Appl. Math. Comput. %D 2004 %V 150 %F Kutluay2004 %0 Journal Article %T Numerical and machine solutions of transient heat-conduction problems involving melting or freezing %A W. D. Murray %A F. Landis %J J. Heat Transfer %D 1959 %V 81 %F Murray1959 %0 Book %T Moving Boundary Problems in Heat Flow and Diffusion %A J. Ockendon %A W. Hodgkins %D 1975 %I Clarendon Press %C Oxford %F Ockendon1975