Polynomial Solutions of Electric Field Equations in Anisotropic Media
Abstract
The time-dependent system of partial differential equations of the second order
describing the electric wave propagation in electrically and magnetically anisotropic
homogeneous media is considered in the paper. A method for the computation of
the polynomial solutions of the initial value problem for the considered system
is proposed. Symbolic computations are used and these symbolic computations
are implemented in Maple. It is proved also that these polynomial solutions are
approximate solutions of the considered initial value problem with smooth initial
data and the inhomogeneous term. The computational experiments confirm the
robustness of the suggested method for the computation of electric fields in general
electrically and magnetically anisotropic media.
Keywords
The timedependent electric field equations, electromagnetic radiation, analytical method, symbolic computations, anisotropic media
References
- [1] Cohen, G. C. (2002). Higher-order numerical methods for transient wave equations. Scientific computation. Springer, Berlin, Heidelberg, New York. [2] Courant, R. and Hilbert, D. (2008). Methods of mathematical physics: partial differential equations. John Wiley & Sons.
- [3] Eom, H. J. (2004). Electromagnetic Wave Theory For Boundary-Value Problems. Springer-Verlag, Berlin.
- [4] Goldberg, J. L. (1991). Matrix Theory with Applications. McGraw-Hill, New York.
- [5] Ikawa, M. (2000). Hyperbolic partial differential equations and wave phenomena, volume 2. American Mathematical Soc.
- [6] Ishimaru, A. (1991). Electromagnetic wave propagation, radiation, and scattering. Prentice Hall.
- [7] Kong, J. A. (1990). Electromagnetic Wave Theory, 2nd ed. Wiley. John Wiley & Sons Inc., New York.
- [8] Mizohata, S. (1973). The theory of partial differential equations. CUP Archive.
- [9] Monk, P. (2003). Finite Element Methods For Maxwell’s Equations. Numerical Mathematics and Scientific Computation. Oxford University Press, New York.
- [10] Neittaanm¨aki, P., Joly, P., Heikkola, E., Cohen, G. C., national de recherche en informatique et en automatique (France), I., and of Jyv¨askyl¨a (FI), U., editors (2003). Mathematical and numerical aspects of wave propagation –WAVES 2003 : proceedings, 6, Jyv¨askyl¨a, FI. Springer.
- [11] Ramo, S., Whinnery, J. R., and Duzer, T. (1994). Fields andWaves in Communication Electronics. Wiley. JohnWiley & Sons Inc., New York.