Far Eastern Mathematical Journal

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Convergence of Newton's method for equations of complex heat transfer


Grenkin G.V.

2017, issue 1, Ñ. 3-10


Abstract
Global monotonic convergence of Newton's method is proved for solving equations of complex heat transfer within the $P_1$

Keywords:
radiative heat transfer, diffusion approximation, Newton's method, monotonic convergence

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References

[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.
[2] A. Astrakhantseva, A. Kovtanyuk, “Numerical modeling the radiative-convective-conduct- ive heat transfer”, 2014 International Conference on Computer Technologies in Physical and Engineering Applications (ICCTPEA), 2014, 106–107.
[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.
[4] A.E. Kovtanyuk, A.Yu. Chebotarev, N.D. Botkin, K.-H. Hoffmann, “Solvability of P1 approximation of a conductive-radiative heat transfer problem”, Appl. Math. Comput., 249, (2014), 247–252.
[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.
[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.
[7] N.L. Schryer, “Newton’s method for nonlinear elliptic boundary value problems”, Numer. Math., 17:4, (1971), 284–300.
[8] E.M. Mukhamadiev, V.Ia. Stetsenko, “Dostatochnye usloviia skhodimosti metoda N'iutona-Kantorovicha pri reshenii kraevykh zadach dlia kvazilineinykh uravnenii ellipticheskogo tipa”, Sib. matem. zhurn., 12:3, (1971), 576–582.
[9] D. Ortega, V. Reinboldt, Iteratsionnye metody resheniia nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975.
[10] F.A. Potra, W.C. Rheinboldt, “On the monotone convergence of Newton’s method”, Computing, 36:1, (1986), 81–90.
[11] T. Gallouet, R. Herbin, A. Larcher, J.-C. Latche, “Analysis of a fractional-step scheme for the P1 radiative diffusion model”, Comput. Appl. Math., 35:1, (2016), 135–151.
[12] E. Zeidler, Nonlinear functional analysis and its applications. II/A: Linear monotone operators, Springer, New York, 1990.

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