Geodesic
A method for the numerical solution of integral equations in boundary value problems with finite-order Abelian symmetry groups
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 11, pp. 1661-1674 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that for boundary value problems with commutative finite-order symmetry groups it is possible to use the concepts of convolution and the Fourier transform for finite groups to reduce considerably the order of the matrix equations used to approximate the original integral equations, and thus to extend the range of problems amenable to numerical analysis. An implementation of this method is considered for boundary value problems with Abelian symmetry group of eighth order, describing a quadrupole-type system. Results of a numerical experiment are presented for this case, enabling the efficiency of the method to be estimated. 
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     title = {A method for the numerical solution of integral equations in boundary value problems with finite-order {Abelian} symmetry groups},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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E. V. Zakharov; S. I. Safronov; R. P. Tarasov. A method for the numerical solution of integral equations in boundary value problems with finite-order Abelian symmetry groups. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 11, pp. 1661-1674. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_11_a5/

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