Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using heat polynomials methods
Kassabek S.A. Suragan D.
June 2022Springer Science and Business Media Deutschland GmbH
Computational and Applied Mathematics
2022#41Issue 4
The paper presents a new approximate method of solving one-dimensional inverse Cauchy–Stefan problems. We apply the heat polynomials method (HPM) for solving the one-dimensional inverse Cauchy–Stefan problem, where the initial and boundary data are reconstructed on a fixed boundary. The solution of the problem is presented in the form of linear combination of heat polynomials. We have studied the effects of accuracy and measurement error for different degree of heat polynomials. Due to ill-conditioning of the matrix generated by HPM, optimization techniques are used to obtain regularized solution. Therefore, the sensitivity of the method to the data disturbance has been checked. Theoretical properties of the proposed method, as well as numerical experiments, demonstrate that to reach accurate results, it is quite sufficient to consider only a few of polynomials.
Approximate solution , Inverse Cauchy–Stefan problem , Method of heat polynomials , Tikhonov regularization
Text of the article Перейти на текст статьи
Astana IT university, Nur-Sultan, Kazakhstan
Department of Mathematics and Natural Sciences, Suleyman Demirel University, Kaskelen, Kazakhstan
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Astana IT university
Department of Mathematics and Natural Sciences
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026