Geodesic
4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients
Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 3-14

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

We present compact difference scheme on three-point stencil for unknown function. The scheme approximates linear second order differential equation with variable smooth coefficient. Our numerical experiments confirmed 4-th accuracy order of solutions of the difference scheme and of eigenvalues’ approximation for the boundary problem. The difference operator is almost self-conjugate, and its spectrum is real. The Richardson extrapolation method improves the accuracy order.
Keywords: compact difference scheme, test functions, self-conjugacy.
Mots-clés : divergent scheme 
@article{MM_2017_29_7_a0,
     author = {V. A. Gordin and E. A. Tsymbalov},
     title = {4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {29},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_7_a0/}
}
TY  - JOUR
AU  - V. A. Gordin
AU  - E. A. Tsymbalov
TI  - 4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 3
EP  - 14
VL  - 29
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_7_a0/
LA  - ru
ID  - MM_2017_29_7_a0
ER  - 
%0 Journal Article
%A V. A. Gordin
%A E. A. Tsymbalov
%T 4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients
%J Matematičeskoe modelirovanie
%D 2017
%P 3-14
%V 29
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_7_a0/
%G ru
%F MM_2017_29_7_a0
V. A. Gordin; E. A. Tsymbalov. 4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients. Matematičeskoe modelirovanie, Tome 29 (2017) no. 7, pp. 3-14. http://geodesic.mathdoc.fr/item/MM_2017_29_7_a0/