Geodesic
Approximate integration of ordinary differential equations using Chebyshev series with precision control
Matematičeskoe modelirovanie, Tome 34 (2022) no. 6, pp. 53-74

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

An approximate method of solving the Cauchy problem for canonical systems of second order ordinary differential equations is considered. The method is based on using the shifted Chebyshev series and a Markov quadrature formula. Some approaches are given to estimate the errors of an approximate solution and its derivative expressed by partial sums of a certain order shifted Chebyshev series. The errors are estimated using the second approximation of the solution calculated in a special way and expressed by a partial sum of a higher order series. An algorithm of partitioning the integration interval into elementary subintervals to ensure the computation of the solution and its derivative with prescribed accuracy is discussed on the basis of proposed approaches to error estimation.
Keywords: ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, polynominal approximation, precision control, error estimate, automatic step size control.
Mots-clés : Markov quadrature formulas 
@article{MM_2022_34_6_a3,
     author = {S. F. Zaletkin},
     title = {Approximate integration of ordinary differential equations using {Chebyshev} series with precision control},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {53--74},
     publisher = {mathdoc},
     volume = {34},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_6_a3/}
}
TY  - JOUR
AU  - S. F. Zaletkin
TI  - Approximate integration of ordinary differential equations using Chebyshev series with precision control
JO  - Matematičeskoe modelirovanie
PY  - 2022
SP  - 53
EP  - 74
VL  - 34
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2022_34_6_a3/
LA  - ru
ID  - MM_2022_34_6_a3
ER  - 
%0 Journal Article
%A S. F. Zaletkin
%T Approximate integration of ordinary differential equations using Chebyshev series with precision control
%J Matematičeskoe modelirovanie
%D 2022
%P 53-74
%V 34
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2022_34_6_a3/
%G ru
%F MM_2022_34_6_a3
S. F. Zaletkin. Approximate integration of ordinary differential equations using Chebyshev series with precision control. Matematičeskoe modelirovanie, Tome 34 (2022) no. 6, pp. 53-74. http://geodesic.mathdoc.fr/item/MM_2022_34_6_a3/