Аннотация:The paper considers a one-dimensional problem for Usadel elliptic equations with nonstandard jump conditions on the inner boundary and a discontinuous solution. The integro-interpolation (balance) method is used for finite difference approximation, including the junction condition on the inner boundary where jump of the solution is proportional to the flux. This difference scheme is used to solve the system of nonlinear Usadel equations, which is the basic mathematical model at the microlevel for describing currents and fields in superconductors, including those with Josephson junctions.
