Computational identification of the boundary condition in the heat transfer problems

  • Efimova Aima M., M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42, Kulakovsky St., Yakutsk 677000, Russia
Keywords: inverse boundary problem, inverse Stefan problem, finite difference method, marching method


The inverse boundary-value problems of heat transfer are of great practical importance, and the work of many authors is devoted to the numerical methods of their solution. We consider a direct method for solving inverse boundary-value problems for a one-dimensional parabolic equation that decomposes a finite-difference analogue of the problem at each time layer. With the help of the proposed numerical solution, we solve the inverse boundary-value problems with a fixed boundary, with a moving boundary, and the Stefan problem. The results of numerical calculations are discussed.


[1]Alekseev A. S., Belonosov V. S., and Glinsky B. M., Methods for Solving Direct and Inverse Problems of Seismology, Electromagnetism, and Experimental Studies in the Problems of Studying Ggeodynamic Processes in the Crust and Upper Mantle of the Earth, Izdat. Vychisl. Tsentra SO RAN, Novosibirsk, 2010
[2]Alifanov O. M., Heat Exchange Inverse Problems, Mashinostroenie Publ., Moscow, 1988
[3]Tikhonov A. N. and Arsenin V. Yu., Solutions of Ill Posed Problems, Nauka, Moscow, 1986  mathscinet
[4]Kabanikhin S. I., Inverse and Ill-posed Problems, Sib. Sci. Publ. House, Novosibirsk, 2009
[5]Samarskiy A. A. and Vabishchevich P. N., Numerical Methods of Solution of Inverse Problems of Mathematical Physics, Izdat. LKI, Moscow, 2009
[6]Kalitkin N. N., Numerical Methods, Nauka, Moscow, 1978  mathscinet
[7]Samarskiy A. A., The Theory of Difference Schemes, Nauka, Moscow, 1977  mathscinet
[8]Vabishchevich P. N., Vasil'ev V. I., and Vasilyeva M. V., Comput. Math. Math. Phys., 55:6 (2015), 1015–1021  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus
[9]Vabishchevich P. N. and Vasil'ev V. I., “Computational determination of the lowest order coefficient in a parabolic equation”, Dokl. Math., 89:2 (2014), 179-181  crossref  crossref  mathscinet  elib  scopus
[10]Vabishchevich P. N., Vasil'ev V. I., “Computational algorithms for solving the coefficient inverse problem for parabolic equations”, Inverse Probl. Sci. Engin., 24:1 (2016), 42–59  crossref  mathscinet  scopus
[11]Vasil'ev V. I., Vasilyeva M. V., Kardashevsky A. M., “The numerical solution of the boundary inverse problem for a parabolic equation”, AIP Conf. Proc., 1773 (2016), 100010  crossref  scopus
[12]Johansson B. T., Lesnic D., Reeve T., “A method of fundamental solutions for the one dimensional inverse Stefan problem”, Appl. Math. Modell., 35:9 (2011), 4367–4378  crossref  mathscinet  elib  scopus
How to Cite
Efimova, A. ( ) “Computational identification of the boundary condition in the heat transfer problems”, Mathematical notes of NEFU, 24(2), pp. 63-74. doi:
Mathematical Modeling