Numerical method for nonlinear eigenvalue problems

A new efficient numerical scheme is presented for analyzing nonlinear boundary value and eigenvalue problems. The method consists of combining the shooting method and Newton's iteration scheme. The method is applied to study the nonlinear interaction of strong laser light with plasma. By the numerical analysis of the structure resonance in laser plasma interaction, multi-valued refraction coefficient as a function of incident laser intensity, and associated anomalous transmission and absorption phenomena are obtained. (Auth.)