On one algorithm for solving the problem of source function reconstruction

Vyacheslav Maksimov

doi:10.2478/v10006-010-0017-3

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On one algorithm for solving the problem of source function reconstruction

International Journal of Applied Mathematics and Computer Science

Volume 20 (2010): Issue 2 (June 2010)

By: Vyacheslav Maksimov

Open Access

|Jul 2010

Abstract

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations in problems data.

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