Geodesic
Nonlinear monotonization of K.\,I.~Babenko scheme for the numerical solution of the advection equation
Matematičeskoe modelirovanie, Tome 16 (2004) no. 6, pp. 44-47

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There are presented the results of constructing of new nonlinear finite-difference scheme for solution a Cauchy problem for linear and quasi-linear advection equation with finite initial data. The scheme is built by means of monotonization of K. I. Babenko (“square”) scheme by introduction of artificial viscosity with “limiters”. 
@article{MM_2004_16_6_a9,
     author = {T. A. Alexandrikova and M. P. Galanin and T. G. Elenina},
     title = {Nonlinear monotonization of {K.\,I.~Babenko} scheme for the numerical solution of the advection equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {44--47},
     publisher = {mathdoc},
     volume = {16},
     number = {6},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_6_a9/}
}
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T. A. Alexandrikova; M. P. Galanin; T. G. Elenina. Nonlinear monotonization of K.\,I.~Babenko scheme for the numerical solution of the advection equation. Matematičeskoe modelirovanie, Tome 16 (2004) no. 6, pp. 44-47. http://geodesic.mathdoc.fr/item/MM_2004_16_6_a9/