The transmutation operator method for efficient solution of the inverse Sturm‐Liouville problem on a half‐line
The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The pote...
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Published in | Mathematical methods in the applied sciences Vol. 42; no. 18; pp. 7359 - 7366 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Freiburg
Wiley Subscription Services, Inc
01.12.2019
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Subjects | |
Online Access | Get full text |
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Summary: | The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The potential q is recovered from the first coefficient of the Fourier‐Legendre series. The resulting numerical method is direct and simple. The results of the numerical experiments are presented. |
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ISSN: | 0170-4214 1099-1476 |
DOI: | 10.1002/mma.5854 |