An inverse problem for computing a leading coefficient in the Sturm–Liouville operator by using the boundary data
Resource
Applied Mathematics and Computation, 218(8), 4245-4259
Journal
Applied Mathematics and Computation
Journal Volume
218
Journal Issue
8
Pages
4245-4259
Date Issued
2011
Date
2011
Author(s)
Liu, Chein-Shan
Abstract
We consider an inverse problem for identifying a leading coefficient α(x) in -(α(x)y′(x))′ + q(x)y(x) = H(x), which is known as an inverse coefficient problem for the Sturm-Liouville operator. We transform y(x) to u(x, t) = (1 + t)y(x) and derive a parabolic type PDE in a fictitious time domain of t. Then we develop a Lie-group adaptive method (LGAM) to find the coefficient function α(x). When α(x) is a continuous function of x, we can identify it very well, by giving boundary data of y, y′ and α. The efficiency of LGAM is confirmed by comparing the numerical results with exact solutions. Although the data used in the identification are limited, we can provide a rather accurate solution of α(x). © 2011 Elsevier Inc. All rights reserved.
Type
journal article
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