Geodesic
Family of fifth-order three-level schemes for evolution problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 2, pp. 206-221

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A multiparameter family of fifth-order three-level schemes in time based on compact approximations is presented for solving evolution problems. The schemes are adapted to hyperbolic and parabolic equations and to stiff systems of ordinary differential equations. In the case of hyperbolic equations, a fifth-order accurate scheme in all variables with compact approximations of spatial derivatives is analyzed. Stability estimates are presented, and the dispersive and dissipative properties are examined. 
@article{ZVMMF_2011_51_2_a1,
     author = {A. I. Tolstykh},
     title = {Family of fifth-order three-level schemes for evolution problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {206--221},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_2_a1/}
}
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A. I. Tolstykh. Family of fifth-order three-level schemes for evolution problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 2, pp. 206-221. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_2_a1/