RETRACTED ARTICLE: A heat polynomials method for the two-phase inverse Stefan problem

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 d...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 42; no. 3
Main Authors Kassabek, Samat A., Suragan, Durvudkhan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2023
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Boundary conditions
Computational mathematics
Computational Mathematics and Numerical Analysis
Inverse problems
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Polynomials
Regularization
80A23
80A22
35C11
Moving boundary
Two-phase inverse Stefan problems
Heat polynomials method
Approximate solution
Heat flux
80M30
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Summary: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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-023-02259-0