Geodesic
Convergence of Newton's method for equations of complex heat transfer
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 1, pp. 3-10.

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Global monotonic convergence of Newton's method is proved for solving equations of complex heat transfer within the $P_1$ approximation of the radiative transfer equation. 
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G. V. Grenkin. Convergence of Newton's method for equations of complex heat transfer. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/DVMG_2017_17_1_a0/

[1] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann, “Unique solvability of a steady-state complex heat transfer model”, Commun. Nonlinear Sci. Numer. Simul., 20:3 (2015), 776–784 | DOI | MR | Zbl

[2] A. Astrakhantseva, A. Kovtanyuk, “Numerical modeling the radiative-convective-conductive heat transfer”, 2014 International Conference on Computer Technologies in Physical and Engineering Applications (ICCTPEA), 2014, 106–107 | DOI

[3] A. E. Kovtanyuk, A. Yu. Chebotarev, “An iterative method for solving a complex heat transfer problem”, Appl. Math. Comput., 219:17 (2013), 9356-9362 | MR | Zbl

[4] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann, “Solvability of $P_1$ approximation of a conductive-radiative heat transfer problem”, Appl. Math. Comput., 249 (2014), 247–252 | MR | Zbl

[5] A. E. Kovtanyuk, A. Yu. Chebotarev, “Nonlocal unique solvability of a steady-state problem of complex heat transfer”, Comput. Math. Math. Phys., 56:5 (2016), 816–823 | DOI | MR | Zbl

[6] A. Yu. Chebotarev, A. E. Kovtanyuk, G. V. Grenkin, N. D. Botkin, K.-H. Hoffmann, “Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model”, Appl. Math. Comput., 289 (2016), 371–380 | MR

[7] N. L. Schryer, “Newton's method for nonlinear elliptic boundary value problems”, Numer. Math., 17:4 (1971), 284–300 | DOI | MR | Zbl

[8] E. M. Mukhamadiev, V. Ya. Stetsenko, “Dostatochnye usloviya skhodimosti metoda Nyutona-Kantorovicha pri reshenii kraevykh zadach dlya kvazilineinykh uravnenii ellipticheskogo tipa”, Sib. matem. zhurn., 12:3 (1971), 576–582 | Zbl

[9] D. Ortega, V. Reinboldt, Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975 | MR

[10] F. A. Potra, W. C. Rheinboldt, “On the monotone convergence of Newton's method”, Computing, 36:1 (1986), 81–90 | DOI | MR | Zbl

[11] T. Gallouët, R. Herbin, A. Larcher, J.-C. Latché, “Analysis of a fractional-step scheme for the $P_1$ radiative diffusion model”, Comput. Appl. Math., 35:1 (2016), 135–151 | DOI | MR | Zbl

[12] E. Zeidler, Nonlinear functional analysis and its applications. II/A: Linear monotone operators, Springer, New York, 1990 | MR | Zbl