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5References
1. Sabelfeld Karl K. Vector Monte Carlo stochastic matrix-based algorithms for large linear systems // Monte Carlo
Methods and Applications, De Gruyter, 2016, v.22 (3), 259-264.
2. Polozhy G. N. On a method for solving integral equations // Izv. Academy of Sciences of the USSR. Ser. Mat. 1959,
v.23, Is. 2, 295-312 [In Russian], (Polozhij G. N. Ob odnom metode resheniya integral'nyh uravnenij // Izv. AN SSSR. Ser.
matem., 1959, Tom. 23, vypusk 2, 295-312).
A randomized iterative method for solving integral equations of the second kind
K. K. Sabelfeld1,2, I. A. Shalimova1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: karl@osmf.sscc.ru, ias@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-90
In this presentation we deal with an extension of the conventional Neumann series based Monte Carlo
method for solving integral equations of the second kind. This approach is based on a randomized evaluation
of the iterative procedure proposed by Polozhy in [1]. In contrast to the simple iteration method, this iterative
procedure converges without any spectral restriction on the integral operator. The major challenge encoun-
tered in the present study is the analysis of the variance behavior as a function of the number of iterations.
Preliminary simulations carried out for boundary integral equations of the potential theory indicates that this
behavior is most likely not linear. A discrete version of this stochastic algorithm implementation of the Polozhy
iterative method has been developed and presented in [3] where a vector randomization of the matrix itera-
tions suggested in [2] has been applied.
This work is supported by the Russian Science Foundation under grant � 19-11-00019, and the Russian Fund of Fun-
damental Studies under Grant 20-51-18009 in the part of random walk process implementations.
References
1. Polozhy G. N. On a method for solving integral equations // Izv. Academy of Sciences of the USSR. Ser. Mat. 1959,
v.23, Is. 2, 295-312 [In Russian], (Polozhij G. N. Ob odnom metode resheniya integral'nyh uravnenij // Izv. AN SSSR. Ser.
matem., 1959, Tom. 23, vypusk 2, 295-312).
2. Sabelfeld Karl K. Vector Monte Carlo stochastic matrix-based algorithms for large linear systems // Monte Carlo
Methods and Applications, De Gruyter, 2016, v.22 (3), 259-264.
Using DSMC calculations to estimate heterogeneous reaction constants based on experimental data
E. V. Shkarupa1, M.Yu. Plotnikov2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Kutateladze Institute of Thermophysics of SB RAS
Email: sev@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-91
The direct simulation Monte Carlo method (DSMC) is widely used in solving problems of the rarefied gas
dynamics. At the present stage, one of the promising areas of its use is the study of the interaction of gas with
surfaces as applied to the problem of gas "activation" on catalytic surfaces. Various approaches to modeling
heterogeneous reactions by the DSMC method are being developed. By virtue of the structure of the DSMC
method, it is fundamental for all the approaches to use microscopic reaction probability when a particle col-
lides with a surface. The amount of data on microscopic probabilities required for modeling heterogeneous
reactions is limited, therefore, the urgent task is to develop approaches for estimating these probabilities
based on experimental data. The work presents the results of using the DSMC method to estimate the micro-
scopic probabilities of heterogeneous reactions based on data obtained by two experimental techniques:
measurement of the gas composition at the outlet of the cylindrical channel and measurement of heat trans-
fer between a heated wire and hydrogen atmosphere.
This work was carried out under state contracts with ICMMG SB RAS (0251-2021-0002) and with IT SB RAS
(121031800218-5).
Economic and mathematical model of the dynamics of the Baikal omul population
P. G. Sorokina1,2, V. I. Zorkaltsev 1,2
1Limnological Institute SBRAS, Irkutsk
2Baikal State University, Irkutsk
Email: sorokinapg@bgu.ru
DOI 10.24412/cl-35065-2021-1-00-92
In 2017, the Russia Government imposes a restrictions on the catches of Baikal omules, which are due to a
significant reduction in its population [1]. By the way, such restrictions led to an increase in poaching and
shadow trade. Unfortunately, the assumed measures have not solved the problem of the recovery of fish
stocks. The development and study of economic measures to regulate the volume of catches of omules would
be useful. The report is devoted to an economic and mathematical model of the development of the stock of
Baikal omule, taking into account both natural fish mortality and the intensity of poaching. At the same time,
the delivery of a commercial omule on the shore of Lake Baikal from other regions and from specially estab-
lished fish-breeding plants is considered to be one of the regulators of catches, as a result of which excessive
catches of omules in oz. Baikal is no longer profitable. The report addresses methodological problems in esti-
mating individual model parameters. [2].
The research was carried out with the financial support of the RFBR project No. 19-07-00322 and within the frame-
work of the project No. state. registration ����-�19-119070190033-0, number MINOBRNAUKI 0279-2019-0003.
References
1. Anoshko P. N., Makarov M.�., V.I. Zorkaltsev, Denikina N.N., Dzyuba E.V. Limits for coregonus migratorius (Georgi,
1775) catches and likely ecological effects. South of Russia: ecology, development 2020 V. 15 no. 3, pp. 132-143.
2. Zorkaltsev V.I. Least squares method: geometric properties, alternative approaches, applications. Novosibirsk:
Nauka, 1995, 220 p.
Vector autoregressive process. Stationarity and modeling
T. M. Tovstik
Saint Petersburg State University
Email: peter.tovstik@mail.ru
DOI 10.24412/cl-35065-2021-1-00-93
The conditions for stationarity of vector processes with a discrete parameter that satisfy the autoregres-
sive equation or a mixed autoregressive and moving average model are investigated. In a mixed model, sta-
