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<p>In this paper we consider the one-phase Stefan problem for melting and solidification in one-space dimension. By using a modified separation of variables method and power series expansion we obtain approximate solutions to this problem. The constructed solutions satisfy all of the boundary and initial conditions. The properties of the solutions are then studied in the context of the corresponding classical problem and error analysis provided. The advantages and the limitations of the procedure are discussed and numerical examples presented.</p>

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Approximate solutions to the one-phase Stefan problem

  • 期刊论文

  • 发表日期：

    2025年12月26日

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  • Vesselin Vatchev

摘要

In this paper we consider the one-phase Stefan problem for melting and solidification in one-space dimension. By using a modified separation of variables method and power series expansion we obtain approximate solutions to this problem. The constructed solutions satisfy all of the boundary and initial conditions. The properties of the solutions are then studied in the context of the corresponding classical problem and error analysis provided. The advantages and the limitations of the procedure are discussed and numerical examples presented.