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A numerical solution to the Gel'fand-Levitan-Marchenko equation
In this paper a numerical method is developed to solve the inverse scattering problem associated with two Gel'fand-Levitan-Marchenko integral equations. This inverse problem is represented by two coupled partial differential equations. The solution of these partial differential equations is two...
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Published in: | Applied mathematics and computation 1998, Vol.89 (1), p.31-39 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | In this paper a numerical method is developed to solve the inverse scattering problem associated with two Gel'fand-Levitan-Marchenko integral equations. This inverse problem is represented by two coupled partial differential equations. The solution of these partial differential equations is two kernel functions. These kernels are also related to each other through the Gel'fand-Levitan-Marchenko integral equations. Legendre-Gauss-Lobatto nodes are used to construct the
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polynominal interpolation to approximate the solution of the kernel functions which are related to the scattering potential. An example is given to demonstrate the accuracy of the proposed method. |
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ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/S0096-3003(97)81646-3 |