Stability of nonlinear iteration in diffusion problems

In this paper, a one dimensional electromagnetic diffusion problem is considered in a half space filled with nonlinear hysteretic media. The material is fed with sinusoidal alternating magnetic field. For the numerical solution of the resulting second order nonlinear partial differential equation, a Finite Difference Time Domain (FDTD) method (the Yee-algorithm) combined with the material Limiting Loop Proximity Hysteresis (LLPH) characteristic is introduced. Stability problems of the numerical method is examined on the basis of the resulted attractor of the iterative map, which exhibits period-doubling bifurcations and chaotic behavior under certain parameter values. The stability analysis based on this attractor is focusing on the reasons behind the instability of the implicit inner iteration.