Inverse problem on the semi-axis: local approach

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Published: Aug 24, 2011
DOI: https://doi.org/10.5556/j.tkjm.42.2011.916
Keywords:
wave equation boundary control method inverse problem Volterra equation Laplace transform numerical analysis

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S. A. Avdonin
University of Alaska Fairbanks, Fairbanks
B. P. Belinskiy
University of Tennessee at Chattanooga
John V. Matthews

Abstract

We consider the problem of reconstruction of the potential for the wave equation on the semi-axis. We use the local versions of the Gelfand-Levitan and Krein equations, and the linear version of Simon's approach. For all methods, we reduce the problem of reconstruction to a second kind Fredholm integral equation, the kernel and the right-hand-side of which arise from an auxiliary second kind Volterra integral equation. A second-order accurate numerical method for the equations is described and implemented. Then several numerical examples verify that the algorithms can be used to reconstruct an unknown potential accurately. The practicality of each approach is briefly discussed. Accurate data preparation is described and implemented.

Article Details

How to Cite
Avdonin, S. A., Belinskiy, B. P., & Matthews, J. V. (2011). Inverse problem on the semi-axis: local approach. Tamkang Journal of Mathematics, 42(3), 275–293. https://doi.org/10.5556/j.tkjm.42.2011.916
Issue
Vol. 42 No. 3 (2011)
Section
Special Issue
Author Biography

John V. Matthews

Assistant professor of Mathematics

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