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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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 42; no. 18; pp. 7359 - 7366
Main Authors Delgado, Briceyda B., Khmelnytskaya, Kira V., Kravchenko, Vladislav V.
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.12.2019
Subjects
Fourier series
Gel'fand‐Levitan equation
half‐line
inverse Sturm‐Liouville problem
Jost solution
Linear algebra
Mathematical analysis
Numerical methods
Operators (mathematics)
spectral density function
Transmutation
transmutation operator
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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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5854