Geodesic
Investigation of an approximate solution of some classes of surface integral equations of the first kind
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 43-54

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A sequence is constructed that converges to an exact solution of a hypersingular integral equation of the first kind of the external Neumann boundary value problem for the Helmholtz equation, which is the boundary value of the solution of the external Neumann boundary value problem on the boundary of the domain. In addition, a sequence is constructed that converges to an exact solution of a weakly singular integral equation of the first kind of the external Dirichlet boundary value problem for the Helmholtz equation, which is the boundary value of the normal derivative of the solution of the external Dirichlet boundary value problem on the boundary of the domain.
Keywords: integral equation of the first kind, weakly singular integral equations, hypersingular integral equations, Helmholtz equation, exterior Neumann boundary-value problem, exterior Dirichlet boundary-value problem. 
@article{VTGU_2021_74_a4,
     author = {E. H. Khalilov},
     title = {Investigation of an approximate solution of some classes of surface integral equations of the first kind},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {43--54},
     publisher = {mathdoc},
     number = {74},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2021_74_a4/}
}
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E. H. Khalilov. Investigation of an approximate solution of some classes of surface integral equations of the first kind. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 43-54. http://geodesic.mathdoc.fr/item/VTGU_2021_74_a4/