At last some decades the series of applied problems (finding: of velocity field when there is the suction of external flow from the serface of streamlined body; of electric field when the current source is placed on absolutely conducting serface; of sound pressure into liqiud layer when the sound source is placed on free serface or on absolutely reflect bottom) lead to necessary of solution of first kind one-dimensional and two-dimensional integral equations in which the kernel has logarithmic singularity (in one-dimensional case) or is weakly singular (in two-dimensional case) , or singular, or hypersingular in class of distributions. In one-dimensional case for mentioned integral equations we must seek the solutions which are delta-functions or having in some points singularity of hyperbola tipe, or discotinuity of first kind.
In the report for characteristic equations in many these cases the analytical solutions are given and the methods of discrete vortex method tipe are suggested for their numerical solution.
Note. Abstracts are published in author's edition
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