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Zbl 1225.35260
Myers, T.G.; Mitchell, S.L.
Application of the combined integral method to Stefan problems. (English)
[J] Appl. Math. Modelling 35, No. 9, 4281-4294 (2011). ISSN 0307-904X

Summary: We present a new, accurate form of the heat balance integral method, termed the combined integral method (CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

MSC 2000:: *35R35 Free boundary problems for PDE
80A22 Stefan problems, etc.
35K05 Heat equation
65M99 Numerical methods for IVP of PDE

Keywords: heat balance integral method; Stefan problems; phase change; perturbation solution

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