A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

Abstract

Purpose The purpose of this paper is to calculate the time-dependent electric and magnetic fields in anisotropic media with a general structure of anisotropy by symbolic computations. Design/methodology/approach An analytical approach for the computation of the time-dependent electric and magnetic fields is suggested. This approach consists of the following. Input data, electric and magnetic fields are presented in polynomial form.The exact formulae for electric and magnetic fields are computed by symbolic transformations in Maple. Findings The time-dependent second order partial differential equations for the electric and magnetic fields with polynomial data were obtained from Maxwell's equations when the current density is presented in a polynomial form with respect to space variables in a bounded region of three dimensional space. The exact solutions of obtained equations were computed symbolically using Maple. Originality/value The obtained polynomial solutions do not contain errors if data are polynomials. We have shown that these solutions are approximate solutions with good accuracy for data which are approximated by polynomials in a bounded region of 3D space.