Geodesic
Features of contrast structure calculation in Cauchy problems
Matematičeskoe modelirovanie, Tome 28 (2016) no. 10, pp. 97-109

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In stiff Cauchy problems solving, we encounter regions where the solution changes very fast. They are called boundary layers. In non-linear problems they can be numerous and take place not only at the initial moment of time but also at following moments. In the latter case, they are called contrast structures. We have shown that in numerical solving of contrast structure problems the round-off errors can become extremely large. Even digit capacity increasing can not resolve this problem. In this case, approximate analytical methods developed in boundary layer theory turn out to be more effective. As an example of applied task, we have considered a real chemical kinetics problem, namely hydrogen in oxygen combustion. A contrast structure appears during such combustion due to production of transitional chemical components. Consequently, real flame burst takes place not instantly but after some time passes.
Keywords: stiff Cauchy problem, contrast structure, boundary layer, chemical kinetics. 
@article{MM_2016_28_10_a7,
     author = {A. A. Belov and N. N. Kalitkin},
     title = {Features of contrast structure calculation in {Cauchy} problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {97--109},
     publisher = {mathdoc},
     volume = {28},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_10_a7/}
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A. A. Belov; N. N. Kalitkin. Features of contrast structure calculation in Cauchy problems. Matematičeskoe modelirovanie, Tome 28 (2016) no. 10, pp. 97-109. http://geodesic.mathdoc.fr/item/MM_2016_28_10_a7/