Geodesic
Two-level schemes of higher approximation order for time-dependent problems with skew-symmetric operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1121-1132 
P. N. Vabishchevich. Two-level schemes of higher approximation order for time-dependent problems with skew-symmetric operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1121-1132. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a11/
@article{ZVMMF_2011_51_6_a11,
     author = {P. N. Vabishchevich},
     title = {Two-level schemes of higher approximation order for time-dependent problems with skew-symmetric operators},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1121--1132},
     year = {2011},
     volume = {51},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a11/}
}
TY  - JOUR
AU  - P. N. Vabishchevich
TI  - Two-level schemes of higher approximation order for time-dependent problems with skew-symmetric operators
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1121
EP  - 1132
VL  - 51
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a11/
LA  - ru
ID  - ZVMMF_2011_51_6_a11
ER  - 
%0 Journal Article
%A P. N. Vabishchevich
%T Two-level schemes of higher approximation order for time-dependent problems with skew-symmetric operators
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1121-1132
%V 51
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a11/
%G ru
%F ZVMMF_2011_51_6_a11

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

Using a model periodic problem for the one-dimensional transport equation as an example, the construction of finite difference time approximations is considered. The emphasis is on the quality criteria of finite difference schemes in what concerns the inheritance of the basic properties of the differential problem, which are related to the transfer of spectral characteristics. Schemes of higher order accuracy based on Padé are analyzed.

[1] Vabischevich P. N., “Dvukhsloinye skhemy povyshennogo poryadka approksimatsii dlya nestatsionarnykh zadach matematicheskoi fiziki”, Zh. vychisl. matem. i matem. fiz., 50:1 (2010), 118–130 | MR

[2] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001

[3] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989

[4] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, URSS, M., 2004

[5] Morton K. W., Numerical solution of convection-diffusion problems, Chapman Hall, London, 1996 | Zbl

[6] Hundsdorfer W., Verwer J., Numerical solution of time-dependent advection-diffusion-reaction equations, Springer, Berlin, 2003 | Zbl

[7] Hirsch C., Numerical computation of internal and external flows. Fundamentals of computational fluid dynamics, Butterworth-Heinemann, Amsterdam, 2007

[8] Gustafsson B., High order difference methods for time dependent PDE, Springer, Berlin, 2008 | Zbl

[9] LeVeque R. J., Finite difference methods for ordinary and partial differential equations. Steady-state and time-dependent problems, Soc. Industr. and Appl. Math. (SIAM), Philadelphia, PA, 2007 | Zbl

[10] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, URSS, M., 2004

[11] Laney C. B., Computational gasdynamics, Cambridge Univ. Press, Cambridge, 1998 | Zbl

[12] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, URSS, M., 2009

[13] Samarskii A. A., Matus P. P., Vabishchevich P. N., Difference schemes with operator factors, Kluwer Acad. Publ., Dordrecht Hardbound, 2002 | Zbl

[14] Hairer E., Wanner G., Solving ordinary differential equations, v. II, Stiff and differential-algebraic problems, Springer, Berlin, 1996 | Zbl

[15] Butcher J. C., Numerical methods for ordinary differential equations, Wiley, Hoboken, NJ, 2008 | Zbl