Geodesic
Modification of finite differences method with use of~Taylor expansions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 152-162.

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

The conducted research compares the method of Taylor expansions and the finite difference method. The obtained method of Taylor expansions employs three, four and five series terms. For each modification a finite difference scheme is presented and its stability, convergence, and approximation are analyzed. For both methods the number of arithmetic operations is counted and compared as well as an error. The advantages of the method of Taylor expansions are revealed.
Keywords: ordinary differential equations, boundary value problem, Taylor series, approximation, stability, finite difference method, method of Taylor expansions, numerical method.
Mots-clés : convergence 
@article{VSGTU_2012_3_a14,
     author = {G. A. Pavlova and I. V. Belyaeva},
     title = {Modification of finite differences method with use {of~Taylor} expansions},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {152--162},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a14/}
}
TY  - JOUR
AU  - G. A. Pavlova
AU  - I. V. Belyaeva
TI  - Modification of finite differences method with use of~Taylor expansions
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2012
SP  - 152
EP  - 162
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a14/
LA  - ru
ID  - VSGTU_2012_3_a14
ER  - 
%0 Journal Article
%A G. A. Pavlova
%A I. V. Belyaeva
%T Modification of finite differences method with use of~Taylor expansions
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2012
%P 152-162
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a14/
%G ru
%F VSGTU_2012_3_a14
G. A. Pavlova; I. V. Belyaeva. Modification of finite differences method with use of~Taylor expansions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 152-162. http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a14/

[1] 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

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

[3] Richtmyer R. D., Morton K. W., Difference methods for initial-value problems, Interscience Tracts in Pure and Applied Mathematics, 4, John Wiley Sons, Inc., New York, London, Sydney, 1967, 405 pp. ; Rikhtmaier R., Morton K., Raznostnye metody resheniya kraevykh zadach, Mir, M., 1972, 421 pp. | MR

[4] Samarskiy A A., Gulin A. V., Numerical methods, Nauka, Moscow, 1989, 432 pp.