Nonlinear boundary condition in electromagnetic theory - Analytical scheme of formulation

The paper presents a method of how the nonlinear boundary condition [1] may be applied in nonlinear problems of electromagnetic field theory. It is introduced for problems with nonlinear conductivity. An analytical procedure has been constructed, which seeks to reduce calculations related with the nonlinear region. In order to verify the proposed solutions, two problems have been formulated: one of linear and the other of cylindrical symmetry. These have been additionally solved by the authors' modification of the perturbation method that has been described in previous papers [7, 8, 10]. The electromagnetic field distribution obtained thereby has served as a referential result since it can obtain very accurate solutions [10]. Relative errors of electric and magnetic field strength are introduced to verify the results.