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

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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/}
}
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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/