This article is cited in 2 papers

Source indentification for the Smoluchowski equation using an ensemble of the adjoint equation solutions

A. V. Penenko^ab, A. B. Salimova<sup>ba

a</sup> Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
^b Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia

Abstract: A source identification algorithm for the systems of nonlinear ordinary differential equations of the production-destruction type is applied to the inverse problem for the discretized Smoluchowski equation. An unknown source function is estimated by time series of measurements of the specific size particles concentration. Based on an ensemble of adjoint equations solutions, the sensitivity operator is constructed that links the perturbations of the sought for model parameters with perturbations of the measured values. This reduces the inverse problem to a family of quasilinear operator equations. To solve the equations, an algorithm of the Newton–Kantorovich type is used with $r$-pseudoinverse matrices. The efficiency and properties of the algorithm are numerically studied.

Key words: Smoluchowsky equation, inverse source problem, Newton–Kantorovich method, adjoint equations, sensitivity operator.

UDC: 517.988, 519.62

Received: 12.12.2018
Revised: 22.03.2019
Accepted: 19.12.2019

DOI: 10.15372/SJNM20200206

 English version: Numerical Analysis and Applications, 2020, 13:2, 152–164

Bibliographic databases:

•