Calculation of currents on the surface of a superconducting axially symmetric body screening an external coaxial magnetic field

A one-dimensional integral equation for the finding of currents on the surface of a superconducting axially symmetric body is given. For the case of an ellipsoid of rotation in a homogeneous magnetic field and for a sphere in a magnetic field with polynomial values on the axis of symmetry, an exact solution is obtained. The axis of symmetry of the body and the axis of the external magnetic field coincide. A numerical algorithm based on a combination of a projective method and an iterative regularization method to solve first kind Fredholm equations is proposed. $B$-splines were chosen as projectors. The results of a numerical reconstruction of the sought-for functions for some particular cases with the use of the method proposed are presented.