Geodesic
kd-Tree based adaptive interpolation algorithm for chemical kinetics problems with interval parameters
Matematičeskoe modelirovanie, Tome 30 (2018) no. 12, pp. 129-144

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In this paper, the question of simulating chemical processes with uncertainty in parameters is considered. A new approach is suggested, which consists in building a dynamic structured net based on a kd-tree, over a space formed by the interval parameters. When the algorithm is executed, during each integration step a piecewise constant polynomial function is build, interpolating the connection between the solution and the exact values of interval parameters. The algorithm has been tested on chemical kinetics problems, including combustion processes, demonstrating its efficiency and wide area of application.
Keywords: interval systems of ODE, dynamic structured grid, chemical kinetics.
Mots-clés : Lotka–Volterra model 
@article{MM_2018_30_12_a7,
     author = {A. Yu. Morozov and D. L. Reviznikov and V. Yu. Gidaspov},
     title = {kd-Tree based adaptive interpolation algorithm for chemical kinetics problems with interval parameters},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {129--144},
     publisher = {mathdoc},
     volume = {30},
     number = {12},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_12_a7/}
}
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A. Yu. Morozov; D. L. Reviznikov; V. Yu. Gidaspov. kd-Tree based adaptive interpolation algorithm for chemical kinetics problems with interval parameters. Matematičeskoe modelirovanie, Tome 30 (2018) no. 12, pp. 129-144. http://geodesic.mathdoc.fr/item/MM_2018_30_12_a7/