Symbolic Computation of an Exact Solution of the Cauchy Problem for the System of Crystal Optics with Polynomial Data

Yakhno, V. G.; Altunkaynak, Meltem

doi:10.1007/978-3-642-00464-3_70

Cited by 2 publications

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References 11 publications

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“…The computation of PSs in the domain of dependence for the system of crystal optics has been reported in the literature . Further, this technique has been applied for solving the initial value problem (IVP) of the Maxwell's equations in general electrically and magnetically anisotropoic media .…”

Section: Introductionmentioning

confidence: 99%

“…The computation of PSs in the domain of dependence for the system of crystal optics has been reported in the literature. 17,18 Further, this technique has been applied for solving the initial value problem (IVP) of the Maxwell's equations in general electrically and magnetically anisotropoic media. 19 We note that in the work 19 Maxwell's equations in isotropic and anisotropic materials have been reduced to the hyperbolic partial differential equations of the second order for electric and magnetic fields.…”

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confidence: 99%

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Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Yakhno

Altunkaynak

2018

Int J Numerical Modelling

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A new method for the computation of a solution of the Maxwell's equations in bi‐anisotropic media with polynomial input is suggested. This method consists of the reduction of Maxwell's equations to a symmetric hyperbolic system of the first‐order partial differential equations. The solutions of the obtained system are constructed by symbolic computation in Maple for the given polynomial data in an explicit form. For the case when input data are given as smooth functions, an interpolation of the data has been made by polynomials and then an approximate solution has been computed by our method. The robustness of the method is confirmed by computational experiments. The comparison of the suggested method with finite difference time domain method has been done.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Yakhno

Altunkaynak

2018

Int J Numerical Modelling

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Polynomial Solutions of Electric Field Equations in Anisotropic Media

Altunkaynak

2024

MANAS Journal of Engineering

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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.

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Symbolic Computation of an Exact Solution of the Cauchy Problem for the System of Crystal Optics with Polynomial Data

Cited by 2 publications

References 11 publications

Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Polynomial Solutions of Electric Field Equations in Anisotropic Media

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