Numerical solution of an inverse problem of determining the parameters of a source of groundwater pollution

A. L. Karchevsky^a, Y. M. Turganbayev^b, S. G. Rakhmetullina^c, ZH. T. Beldeubayeva<sup>c

a</sup> Sobolev Institute of Mathematics SB RAS, Russia, 630090 Novosibirsk, pr. Koptyuga, 4
^b Graduate School of Business, Nazarbayev University, Kazakhstan, 010000 Astana, Kabanbay Batyr Ave, 53, block C3
^c D. Serikbayev East Kazakhstan State Technical University, Kazakhstan, 070004 Ust-Kamenogorsk, st. A.K. Protozanova, 69

Abstract: The article deals with an inverse problem of determining parameters of ground-water pollution sources. We test three ways to solve the problem on the simulated data for a simple case of contamination. We discover that, in the presence of noise in the data of the inverse problem, the first method does not produce satisfactory recovery results, while the second and third ones are comparable in accuracy of the recovery of required parameters. Taking into account the ease of implementation, the speed of computing and parallelization feasibility the second method of solving the inverse problem is found to be most preferable. We also propose a method of finding pollution parameters in general case.

Keywords: inverse problem, groundwater pollution, Volterra integral equation of the 1-st kind.

MSC: 35K20, 35R30

Received: 11.10.2016

Language: English