Geodesic
A method of obtaining analytical solutions to boundary value problems based on defining additional boundary conditions and additional desired functions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 2, pp. 153-165 
I. V. Kudinov; E. V. Kotova; V. A. Kudinov. A method of obtaining analytical solutions to boundary value problems based on defining additional boundary conditions and additional desired functions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 2, pp. 153-165. http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a3/
@article{SJVM_2019_22_2_a3,
     author = {I. V. Kudinov and E. V. Kotova and V. A. Kudinov},
     title = {A method of obtaining analytical solutions to boundary value problems based on defining additional boundary conditions and additional desired functions},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {153--165},
     year = {2019},
     volume = {22},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a3/}
}
TY  - JOUR
AU  - I. V. Kudinov
AU  - E. V. Kotova
AU  - V. A. Kudinov
TI  - A method of obtaining analytical solutions to boundary value problems based on defining additional boundary conditions and additional desired functions
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2019
SP  - 153
EP  - 165
VL  - 22
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a3/
LA  - ru
ID  - SJVM_2019_22_2_a3
ER  - 
%0 Journal Article
%A I. V. Kudinov
%A E. V. Kotova
%A V. A. Kudinov
%T A method of obtaining analytical solutions to boundary value problems based on defining additional boundary conditions and additional desired functions
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2019
%P 153-165
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a3/
%G ru
%F SJVM_2019_22_2_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Using additional boundary conditions and additional unknown functions in the integral method of heat balance, we consider the method of obtaining analytical solutions to the thermal conductivity problem associated with the separation process of thermal conductivity of two phases with respect to time, which allows reducing the solution of partial differential equations to the integration of two ordinary differential equations for some additional desired functions. The first stage is characterized by a rapid convergence of the analytical solution to an exact one. For the second stage, the exact analytical solution has been obtained. Additional boundary conditions for both phases are in such a form that their execution by a desired solution be equivalent to realization of the original equation at boundary points and at a front of the temperature perturbations. It is shown that the implementation of the equations at the boundary points leads to its execution also inside the domain.

[1] Kudinov V.A., Kudinov I.V., Analiticheskie resheniya parabolicheskih i giperbolicheskih uravneniy teplomassoperenosa, Infra-M, M., 2013

[2] Lykov A.V., “Metody resheniya nelineynyh uravneniy nestatsionarnoy teploprovodnosti”, Energetika i transport, 1970, no. 5, 109–150 | Zbl

[3] Gudmen T., “Primenenie integral'nyh metodov v nelineynyh zadachah nestatsionarnogo teploobmena”, Problemy teploobmena, Sb. nauchnyh trudov, Atomizdat, M., 1967, 41–96

[4] Kudinov V.A., Kudinov I.V., Skvortsova M.P., “Generalized functions and additional boundary conditions in heat conduction problems for multilayered bodies”, Comput. Maths. Math. Phys., 55:4 (2015), 666–676 | DOI | MR | Zbl

[5] Kantorovich L.V., “Ob odnom metode priblizhennogo resheniya differentsial'nyh uravneniy v chastnyh proizvodnyh”, DAN SSSR, 2:9 (1934), 532–534

[6] Fedorov F.M., Granichnyy metod resheniya prikladnyh zadach matematicheskoy fiziki, Nauka, Novosibirsk, 2000

[7] Kudryashov L.I., Men'shih N.L., Priblizhennye resheniya nelineynyh zadach teploprovodnosti, Mashinostroenie, M., 1979

[8] Lykov A.V., Teoriya teploprovodnosti, Vysshaya shkola, M., 1967