TY - JOUR
T1 - A heat polynomials method for the two-phase inverse Stefan problem
AU - Kassabek, Samat A.
AU - Suragan, Durvudkhan
N1 - Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
PY - 2023/4
Y1 - 2023/4
N2 - 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.
AB - 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.
KW - Approximate solution
KW - Heat flux
KW - Heat polynomials method
KW - Moving boundary
KW - Two-phase inverse Stefan problems
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U2 - 10.1007/s40314-023-02259-0
DO - 10.1007/s40314-023-02259-0
M3 - Article
AN - SCOPUS:85150998079
SN - 2238-3603
VL - 42
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 3
M1 - 129
ER -