FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
An iterative algorithm for solving an initial-boundary value problem for a quasi-linear model of complex heat transfer |
Park N.M., Kovtanyuk A.E. |
2023, issue 2, P. 240-245 DOI: https://doi.org/10.47910/FEMJ202320 |
Abstract |
| An initial-boundary value problem for a system of quasilinear equations of radiative-conductive heat transfer, simulating the process of endovenous laser ablation, is considered. An algorithm for finding its solution is proposed and its convergence is proved. The efficiency of the algorithm is illustrated by numerical experiments. |
Keywords: endovenous laser ablation, radiative-conductive heat transfer, iterative algorithm, nonlocal solvability. |
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References |
| [1] A. Yu. Chebotarev, G. V. Grenkin, A. E. Kovtanyuk, N. D. Botkin, K.-H. Hoffmann, “Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions”, Commun. Nonlinear Sci. Num. Simulat., 57 (2018), 290–298. [2] A. Yu. Chebotarev, “Inhomogeneous problem for quasi-stationary equations of complex heat transfer with reflection and refraction conditions”, Comput. Math. Math. Phys., 63 (2023), 441–449. [3] A. A. Poluektova, W. S. J. Malskat , M. J. C.van Gemert, M. E. Vuylsteke, C. M. A. Bruijninckx, H. A. M. Neumann, C.W. M. van der Geld, “Some controversies in endovenous laser ablation of varicose veins addressed by optical-thermal mathematical modeling”, Lasers Med. Sci., 29 (2014), 441–452. |