Geodesic
Error Estimate of Numerical Method for Solving an Inverse Problem
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 3, pp. 51-58

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Linear differential operator and the system of boundary conditions were considered. The boundary conditions are linear and linear independent functionals. The Green functions for the boundary problem defined by this operator and the functionals was build as a solution of the Fredholm integral equation of the second kind. Characteristics of the Fredholm equation was defined by the Green function of the auxiliary problem. The suggested method enables to solve both direct (the problem of finding solutions) and inverse (the problem of finding the right part of the equation from the experimentally obtained solution) problems. The characteristics of the numerical implementation of the method and the possibility of assessing the accuracy of the solutions were discussed.
Keywords: boundary problem, integral equations, Green's function. 
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     author = {V. I. Zalyapin and Yu. S. Popenko and Ye. V. Kharitonova},
     title = {Error {Estimate} of {Numerical} {Method} for {Solving} an {Inverse} {Problem}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a4/}
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V. I. Zalyapin; Yu. S. Popenko; Ye. V. Kharitonova. Error Estimate of Numerical Method for Solving an Inverse Problem. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 3, pp. 51-58. http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a4/