A numerical method based on integro-differential formulation for solving a one-dimensional Stefan problem. (English) Zbl 1142.65079
Summary: A numerical method based on an integro-differential formulation is proposed for solving a one-dimensional moving boundary Stefan problem involving heat conduction in a solid with phase change. Some specific test problems are solved using the proposed method. The numerical results obtained indicate that it can give accurate solutions and may offer an interesting and viable alternative to existing numerical methods for solving the Stefan problem.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 35R35 | Free boundary problems for PDEs |
| 80A22 | Stefan problems, phase changes, etc. |
| 80M25 | Other numerical methods (thermodynamics) (MSC2010) |
Keywords:
integro-differential equation; local interpolating functions; predictor-corrector approach; moving boundary Stefan problem; heat conduction; phase change; numerical resultsReferences:
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