DOI: 10.1515/jiip-2021-0077 ISSN: 0928-0219

Analytical solution of Stefan-type problems

Samat A. Kassabek, Targyn A. Nauryz, Amankeldy Toleukhanov
  • Applied Mathematics


In this paper, free surface problems of Stefan type for the parabolic heat equation are considered. The analytical solutions of the problems are based on the method of heat polynomials and integral error function in the form of series. Convergence of the series solution is considered and proved. Both one-and two-phase Stefan-type problems are investigated. Numerical results for one-phase inverse Stefan problem are presented and discussed.

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