Abstract
The paper considers the problem of the linear charge density reconstruction in a straight conductor according to the known potential on the surface of a virtual cylinder with an axis which coincides with the conductor. The resulting Fredholm integral equation of one kind is the ill-posed problem. The approximate method of determining the unknown function, which is based on Gauss quadrature formulas and interpolation is proposed. The expressions for the coefficients of the system of linear algebraic equations defining the values of the unknown function at the nodes of Gauss are given. The limits of this method applicability are explored. The numerical results of the problem solution for the case when the cylinder is set in a virtual permanent capacity, the sinusoidal potential and the potential with a linear function of the coordinates are presented. It is shown that the greatest deviation from the predetermined received function is observed near the ends of the cylinder.
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