A heat polynomials method for the two-phase inverse Stefan problem

Kassabek S.A. Suragan D.
April 2023 Springer Nature

Computational and Applied Mathematics
2023 #42 Issue 3

In this paper, we extend the heat polynomials method (HPM) proposed by the authors for one-dimensional one-phase inverse Stefan problem to the two-phase case. The solution of the problem is presented in the form of linear combination of heat polynomials. The coefficients of this combination can be determined by satisfying the initial and boundary conditions or by the least square method for the boundary of a domain. The inverse problem is ill-posed, therefore, the regularization will be taken into account. Our numerical results are compared with results obtained by another method and show good enough accuracy.

Approximate solution , Heat flux , Heat polynomials method , Moving boundary , Two-phase inverse Stefan problems

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Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Department of Computational and Data Science, Astana IT University, Nur-Sultan, Kazakhstan
Department of Mathematics and Natural Sciences, Suleyman Demirel University, Kaskelen, Kazakhstan

Department of Mathematics
Department of Computational and Data Science
Department of Mathematics and Natural Sciences

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