A collocation heat polynomials method for one-dimensional inverse Stefan problems
Narbek O. Kassabek S.A. Nauryz T.
1 May 2025Elsevier B.V.
Journal of Computational and Applied Mathematics
2025#460
The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux P(t) with a known moving boundary position s(t), is investigated. A previous study (Kassabek et al., 2021) attempted to reconstruct the unknown heat flux P(t) using the Variational Heat Polynomials Method (VHPM). In this paper, we develop the Collocation Heat Polynomials Method (CHPM) for the reconstruction of the time-dependent heat flux P(t). This method constructs an approximate solution as a linear combination of heat polynomials, which satisfies the heat equation, with the coefficients determined using the collocation method. To address the resulting ill-posed problem, Tikhonov regularization is applied. As an application, we demonstrate the effectiveness of the method on benchmark problems. Numerical results show that the proposed method accurately reconstructs the time-dependent heat flux P(t), even in the presence of significant noise. The results are also compared with those obtained in Kassabek et al. (2021) using the VHPM.
Approximate solution , Heat polynomials method , Inverse Stefan problems , Moving boundary
Text of the article Перейти на текст статьи
SDU University, Department of Mathematics, Almaty, Kazakhstan
Astana IT university, Department of Computational and Data Science, Astana, Kazakhstan
Kazakh British Technical University, Institute of Mathematics and Mathematical Modeling, Narxoz University, Almaty, Kazakhstan
SDU University
Astana IT university
Kazakh British Technical University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026