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Accessible Unlicensed Requires Authentication Published by De Gruyter July 15, 2015

Numerical solution of an inverse problem of coefficient recovering for a wave equation by a stochastic projection methods

Sergey I. Kabanikhin, Karl K. Sabelfeld, Nikita S. Novikov and Maxim A. Shishlenin

Abstract

An inverse problem of reconstructing the two-dimensional coefficient of the wave equation is solved by a stochastic projection method. We apply the Gel'fand–Levitan approach to reduce the nonlinear inverse problem to a family of linear integral equations. The stochastic projection method is applied to solve the relevant linear system. We analyze the structure of the problem to increase the efficiency of the method by constructing an improved initial approximation. A smoothing spline is used to treat the random errors of the method. The method has low cost and memory requirements. Results of numerical calculations are presented.

Funding source: RFBR

Award Identifier / Grant number: 15-01-09230

Funding source: Ministry of Education and Science of the Russian Federation

Funding source: RFBR

Award Identifier / Grant number: 15-01-00977

Funding source: Ministry of Education and Science of the Republic of Kazakhstan

Award Identifier / Grant number: 1746/GF “Theory and numerical methods for solving inverse and ill-posed problems of natural sciences”

Received: 2015-2-9
Accepted: 2015-6-23
Published Online: 2015-7-15
Published in Print: 2015-9-1

© 2015 by De Gruyter