Numerical solution of the multidimensional Gelfand–Levitan equation
2015 ◽
Vol 23
(5)
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Keyword(s):
AbstractThe coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented.
2021 ◽
Vol 2092
(1)
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pp. 012022
1985 ◽
Vol 25
(3)
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pp. 15-23
2020 ◽
Keyword(s):
2016 ◽
Vol 27
(11)
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pp. 1650134
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2008 ◽
Vol 204
(1)
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pp. 1-9
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Keyword(s):
1983 ◽
Vol 16
(18)
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pp. 4423-4426
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Keyword(s):
Keyword(s):