The charged conductor inside dielectric. Solution of the boundary condition by means of auxiliary charges and the method of linear algebraic equations

The present report is devoted to the solution of a problem of conductor in surroundings of a dielectric. The mathematical model - a set of equations describing conditions on the boundary of the dielectric and conductor is presented according to a physical analog. The method is illustrated by an example of the solution of the problem by the way of a digital simulation on the basis of several variants of the physical model. On contrast to our previous publications the way of finding allocations not only electric fields but also potentials is considered. The method is supposed to be used for simulation of electric fields of the detector ZEPLIN III on search for corpuscular 'dark matter'