..

2017, 1, . 3-10


$P_1$-

:
, , ,

( PDF)

[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), 776784.
[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, 106107.
[3] A.E. Kovtanyuk, A.Yu. Chebotarev, An iterative method for solving a complex heat transfer problem, Appl. Math. Comput., 219:17, (2013), 93569362.
[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), 247252.
[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), 816823.
[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), 371380.
[7] N.L. Schryer, Newtons method for nonlinear elliptic boundary value problems, Numer. Math., 17:4, (1971), 284300.
[8] .. , .. , - , . . ., 12:3, (1971), 576582.
[9] . , . , , , ., 1975.
[10] F.A. Potra, W.C. Rheinboldt, On the monotone convergence of Newtons method, Computing, 36:1, (1986), 8190.
[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), 135151.
[12] E. Zeidler, Nonlinear functional analysis and its applications. II/A: Linear monotone operators, Springer, New York, 1990.