Geodesic
Boundary value problems solving method with the implicit use of the Taylor expansions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 227-232.

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

Grid method for boundary value problems solving for partial differential equations based on high order Taylor expansions is suggested. Comparison of the proposed method with classical grid method is implemented. It is shown that the use of the Taylor expansion with specified partial differential equations allows to reduce the estimated faulty proportion of the numerical solution for a given constant sampling area by increasing the order of the expansion. A number of model boundary value problems is solved, the results of the estimated faulty proportion are given.
Keywords: partial differential equations, boundary value problem, Taylor expansion, the grid method, approximation, estimated faulty proportion. 
@article{VSGTU_2012_4_a24,
     author = {A. A. Usov},
     title = {Boundary value problems solving method with the implicit use of the {Taylor} expansions},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {227--232},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a24/}
}
TY  - JOUR
AU  - A. A. Usov
TI  - Boundary value problems solving method with the implicit use of the Taylor expansions
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2012
SP  - 227
EP  - 232
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a24/
LA  - ru
ID  - VSGTU_2012_4_a24
ER  - 
%0 Journal Article
%A A. A. Usov
%T Boundary value problems solving method with the implicit use of the Taylor expansions
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2012
%P 227-232
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a24/
%G ru
%F VSGTU_2012_4_a24
A. A. Usov. Boundary value problems solving method with the implicit use of the Taylor expansions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 227-232. http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a24/

[1] Usov A. A., “On one approach to the numerical solution of boundary value problems on the basis of Taylor's formula”, Proceedings of the Eighth Inter-University Conference. Part 3, Matem. Mod. Kraev. Zadachi, Samara State Technical Univ., Samara, 1998, 99–102

[2] Usov A. A., Radchenko V. P., “On one approach to the solution of boundary value problems for equations of mathematical physics with use of Taylor expansions”, Proceedings of the Sixth All-Russian Scientific Conference with international participation (1–4 June 2009). Part 1, Matem. Mod. Kraev. Zadachi, Samara State Technical Univ., Samara, 2009, 271–276

[3] Radchenko V. P., Usov A. A., “Modified grid method for solving linear differential equation equipped with variable coefficients based on Taylor series”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2008, no. 2(17), 60–65 | DOI | MR

[4] Pavlova G. A., Belyaeva I. V., “Modification of finite differences method with use of Taylor expansions”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2012, no. 3(28), 152–162 | DOI | MR

[5] Volkov E. A., Numerical methods, Lan', Moscow, 2004, 256 pp. | Zbl