Superconsistent discretizations with application to hyperbolic equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 1, pp. 89-99.

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

A family of finite difference methods for the linear hyperbolic equations, constructed on a six-point stencil, is presented. The family depends on 3 parameters and includes many of the classical linear schemes. The approximation method is based on the use of two different grids. One grid is used to represent the approximated solution, the other (the collocation grid) is where the equation is to be satisfied. The two grids are related in such a way that the exact and the discrete operators have a common space which is as large as possible.
@article{SJVM_2003_6_1_a6,
     author = {Daniele Funaro},
     title = {Superconsistent discretizations with application to hyperbolic equation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {89--99},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2003_6_1_a6/}
}
TY  - JOUR
AU  - Daniele Funaro
TI  - Superconsistent discretizations with application to hyperbolic equation
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2003
SP  - 89
EP  - 99
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2003_6_1_a6/
LA  - en
ID  - SJVM_2003_6_1_a6
ER  - 
%0 Journal Article
%A Daniele Funaro
%T Superconsistent discretizations with application to hyperbolic equation
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2003
%P 89-99
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2003_6_1_a6/
%G en
%F SJVM_2003_6_1_a6
Daniele Funaro. Superconsistent discretizations with application to hyperbolic equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 1, pp. 89-99. http://geodesic.mathdoc.fr/item/SJVM_2003_6_1_a6/

[1] Funaro D., Spectral Elements for Transport-Dominated Equations, LNCS, 1, Springer, 1997 | MR

[2] Funaro D., “A note on second-order finite-difference schemes on uniform meshes for advectiondiffusion equations”, Num. Meth. PDEs, 15 (1999), 581–588 | MR | Zbl

[3] Funaro D., “Superconsistent discretizations”, J. of Scientific Computing, 17:1–4 (2002), 67–79 | DOI | MR | Zbl

[4] Funaro D., Pontrelli G., A general class of finite-difference methods for the linear transport equation (to appear)

[5] Godunov S. K., Ryabenkii V. S., Difference Schemes: an Introduction to the Underlying Theory, North Holland, New York, 1987 | MR | Zbl

[6] Il'in A. M., “Differencing scheme for a differential equation with a small parameter affecting the highest derivative”, Math. Notes Acad. Sci. USSR, 6 (1969), 596–602 | DOI | MR

[7] Strikwerda J. C., Finite Difference Schemes and Partial Differential Equations, Chapman Hall, 1989 | MR