Geodesic
Monotonization of a family of implicit schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 672-679

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An algorithm is proposed for monotonizing the correction of implicit schemes with high order of approximation of the space derivatives. The transport equation with one space variable is used as an example to prove that the corrected schemes are indeed monotone, provided that the time-step is restricted. 
@article{ZVMMF_1990_30_5_a3,
     author = {V. I. Pinchukov},
     title = {Monotonization of a~family of implicit schemes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {672--679},
     publisher = {mathdoc},
     volume = {30},
     number = {5},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a3/}
}
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V. I. Pinchukov. Monotonization of a family of implicit schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 672-679. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a3/