Open AccessNUMERICAL ALGORITHM FOR SOLVING THE CONTINUATION PROBLEM FOR THE ACOUSTIC EQUATION
Author(s) -
Janar Askerbekova
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-2.1728-7901.01
Subject(s) - inverse problem , mathematics , rate of convergence , continuation , nonlinear system , convergence (economics) , boundary value problem , iterative method , algorithm , numerical analysis , minification , initial value problem , mathematical optimization , computer science , mathematical analysis , computer network , channel (broadcasting) , physics , quantum mechanics , economics , programming language , economic growth
In this paper we consider the initial-boundary value problem for the acoustics equation in the temporal-triangular domain. We reduce the original ill-posed problem to an equivalent inverse problem with respect to some direct problem. This direct problem is well-posed. The inverse problem is replaced by a minimization problem. An algorithm for solving the inverse problem by the Landweber iteration method is constructed. We apply the method of successive approximations to the equation, we obtain a natural extension to nonlinear problems. This method leads to optimal convergence rate in certain cases. An analysis of the iterative Landweber method for nonlinear problems depends on the source conditions and additional conditions. Convergence analysis and error estimates are usually made with many assumptions, which are very difficult to verify from a practical point of view. This method leads to optimal convergence rate under certain conditions. Theoretical analysis is confirmed by numerical results. Visual examples are processed numerically.