Geodesic
On difference schemes for quasilinear evolution problems
Electronic transactions on numerical analysis, Tome 27 (2007), pp. 78-93
We review several methods leading to variable-coefficient schemes and/or to exact difference schemes for ordinary differential equations (error elimination; functional fitting; Principle of Coherence). Necessary and suffient conditions are given for -independence of fitted RK coefficients. Conditions for -independence are inves- $\textcent \sterling $tigated, the time-step. The theory is illustrated by examples. In particular, examples are given for non-uniqueness $\sterling $of exact schemes and for efficient difference schemes based on exact schemes and well suited for highly oscillatory ordinary differential systems or for parabolic equations with blow-up solutions.
Classification : 65L05, 65M06, 65P99
Keywords: difference schemes, time stepping, nonstandard schemes, exact schemes, exponential Fitting, functional Fitting, Runge-Kutta, collocation methods, review 
@article{ETNA_2007__27__a6,
     author = {Meyer-Spasche,  Rita},
     title = {On difference schemes for quasilinear evolution problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {78--93},
     year = {2007},
     volume = {27},
     zbl = {1171.65414},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__27__a6/}
}
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Meyer-Spasche,  Rita. On difference schemes for quasilinear evolution problems. Electronic transactions on numerical analysis, Tome 27 (2007), pp. 78-93. http://geodesic.mathdoc.fr/item/ETNA_2007__27__a6/