Numerical methods of solution for heat equation with delay
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 113-116
V. G. Pimenov. Numerical methods of solution for heat equation with delay. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 113-116. http://geodesic.mathdoc.fr/item/VUU_2008_2_a36/
@article{VUU_2008_2_a36,
     author = {V. G. Pimenov},
     title = {Numerical methods of solution for heat equation with delay},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {113--116},
     year = {2008},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2008_2_a36/}
}
TY  - JOUR
AU  - V. G. Pimenov
TI  - Numerical methods of solution for heat equation with delay
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2008
SP  - 113
EP  - 116
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VUU_2008_2_a36/
LA  - ru
ID  - VUU_2008_2_a36
ER  - 
%0 Journal Article
%A V. G. Pimenov
%T Numerical methods of solution for heat equation with delay
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2008
%P 113-116
%N 2
%U http://geodesic.mathdoc.fr/item/VUU_2008_2_a36/
%G ru
%F VUU_2008_2_a36

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

Numerical methods of solution are designed for the equation of heat conductivity with effect of delay. The method of straight lines and the implicit scheme with piece- constant interpolation are considered. The theorem of convergence of the last method is presented.

[1] Wu J., Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, N.Y., 1996 | MR

[2] Tavernini L., “Finite Difference Approximations for a Class of Semilinear Volterra Evolution Problems”, SIAM J. Numer. Anal., 14:5 (1977), 931–949 | DOI | MR | Zbl

[3] Kim A. V., Pimenov V. G., $i$-gladkii analiz i chislennye metody resheniya funktsionalno-differentsialnykh uravnenii, Regulyarnaya i khaoticheskaya dinamika, Izhevsk, Moskva, 2004

[4] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999