Geodesic
Bases derived from trigonometry and their advantages
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 105-119

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

A specific use of trigonometric functions with respect to any interval possesses a high approximate quality. In this case, a solution of integral equations with kernels of the form $K(x-t)$ by the Galerkin method allows one to reduce the double integral to a very simple single integration. Also, a specific base of functions for solving problems with an elliptic operator with disconnected coefficients is proposed. A distinctive feature of this base is automatic realization of conjugate conditions in locations of discontinuities of coefficients of equations. Another essential property is a high-precise approximation of piecewise-smooth solutions of the above problems by means of a small number of base functions. All the proofs of the results obtained follow from the two theorems presented.
Keywords: problems with elliptic operator, discontinuous coefficients, piecewise-smooth basis functions, rapidly convergent series, approximation, minimization of square functional, integral equations
Mots-clés : conjugate conditions. 
@article{VNGU_2013_13_1_a9,
     author = {V. V. Smelov},
     title = {Bases derived from trigonometry and their advantages},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {105--119},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a9/}
}
TY  - JOUR
AU  - V. V. Smelov
TI  - Bases derived from trigonometry and their advantages
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2013
SP  - 105
EP  - 119
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a9/
LA  - ru
ID  - VNGU_2013_13_1_a9
ER  - 
%0 Journal Article
%A V. V. Smelov
%T Bases derived from trigonometry and their advantages
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2013
%P 105-119
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a9/
%G ru
%F VNGU_2013_13_1_a9
V. V. Smelov. Bases derived from trigonometry and their advantages. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 105-119. http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a9/