FINITE DIFFERENCES SCHEME FOR DISCONTINUOUS SOLUTIONS OF USADEL EQUATIONS

In the paper we consider a nonlinear one-dimensional problem for equations of superconductivity theory. The peculiarity of the problem is a nonstandard Roben type junction condition on the inner boundary and a discontinuous solution. An optimal homogeneous monotone difference scheme including the condition at the interface is constructed for the problem. By means of solving a series of elliptic problems and Newton’s method, we solve the complete system of the Uzadel equations, which is the basic mathematical model at the microlevel for describing the currents and fields in superconductors with Josephson junctions. The results of calculations for the problem of a pellet with an Apricot vortex are presented.