Abstract
In this paper an explicit scheme for solving numerically an inverse scattering problem is proposed. An estimate of the difference solution has been obtained by using discrete Gelfand-Levitan equations and two derived equations, and two criteria for stability have been found. Several numerical experiments give strong support to our investigation.
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References
I.M. Gelfand & B.M. Levitan On the determination of differential equation from its spectral function Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951) p309
W. Symes Numerical stability in an inverse scattering problem SIAM J. Numer. Anal. vol.17 No 5 (1980) p707
K.P. Bube & R. Burridge The one-dimensional inverse problem of reflection seismology SIAM Rev. vol 25 No 4 (1983) p497
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© 1987 Springer-Verlag
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Zhu, Br., Jin, My. (1987). An explicit scheme for an inverse scattering problem and its stability analysis. In: Zhu, YI., Guo, By. (eds) Numerical Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078551
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DOI: https://doi.org/10.1007/BFb0078551
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Print ISBN: 978-3-540-18730-1
Online ISBN: 978-3-540-48126-3
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