Title: A numerical algorithm for solving an inverse semilinear wave problem

Authors: Reza Pourgholi; Amin Esfahani; Sunil Kumar

Addresses: School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran ' School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran ' Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India

Abstract: The problem of identifying the solution (k(x, t),U(x, t)) in an inverse semilinear wave problem is considered. It is shown that under certain conditions of data φ, ψ, there exists a unique solution (k(x, t),U(x, t)) of this problem. Furthermore a numerical algorithm for solving the inverse semilinear wave problem is proposed. The approach for this inverse problem is given by using the semi-discretisation method. A polynomial function is proposed to approximate U(x, t) then the finite difference method is applied to approximate unknown k(x, t). Numerical results show efficiency of our method.

Keywords: inverse semilinear wave problem; finite difference method; stability; uniqueness; polynomial function; semi-discretisation.

DOI: 10.1504/IJCSM.2014.059378

International Journal of Computing Science and Mathematics, 2014 Vol.5 No.1, pp.1 - 15

Received: 28 Aug 2012
Accepted: 17 Mar 2013
Published online: 30 Jun 2014 *

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