Improvements of Approximating Functions Method for Solving Problems with a Dielectric Layer with Media of a High Degree of Nonlinearity

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The article introduces analytical modifications of the approximating functions method, a special case of finite element method (FEM), which entail an increase in its computational performance for solving electrodynamics problems in one space dimension and time domain (1D+T) inside inhomogeneity with nonlinear media placed in the linear one, using the Volterra integral equation method, which is an integral equations equivalent to Maxwell's equations. The purpose of this study is not only to make the analytical improvements, but also to adapt them for fast and convenient programming and fast computations. The proposed method was validated on the problems of interaction of electromagnetic waves incident on a layer with second-order and third-order nonlinear medium inserted in linear media.