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A second order difference scheme for one-dimensional Stefan problem. (English) Zbl 1240.65259

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
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