Wang, Jialing; Sun, Zhizhong A second order difference scheme for one-dimensional Stefan problem. (English) Zbl 1240.65259 J. Nanjing Univ., Math. Biq. 27, No. 2, 218-229 (2010). Summary: This article is concerned with the numerical solution of the classical one dimensional phase Stefan problem. A Landau-type transformation is introduced to make the problem on a fixed domain. A new function transformation is introduced to make the nonlinear boundary condition be a linear one. A linearized three-level difference scheme of Crank-Nicolson-type is constructed to determine the temperature distribution and the position of the moving boundary. The unique solvability of the difference scheme is proved by the energy method. A numerical example is presented to demonstrate the unconditional stability and second-order convergence of the finite difference scheme. MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 80A22 Stefan problems, phase changes, etc. 35K05 Heat equation 35R35 Free boundary problems for PDEs Keywords:Stefan problem; Landau transformation; difference scheme; unique solvability; stability; convergence; nonlinear boundary condition; Crank-Nicolson-type; moving boundary; energy method; numerical example PDFBibTeX XMLCite \textit{J. Wang} and \textit{Z. Sun}, J. Nanjing Univ., Math. Biq. 27, No. 2, 218--229 (2010; Zbl 1240.65259)