On Maxwell's equations in non-stationary media

Maxwell's equations formulated for media with gradually changing conductivity are reduced to Volterra integral equations. Analytical and numerical investigations of the equations are presented for the case of gradual splash-like change in conductivity. Splash-like change in medium parameters can model any discharge phenomena, growing plasma, charge injection, etc. Exact analytical solution for the resolvent is presented and different field behaviours are analysed for the incident field as a plane wave and as an impulse.

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Calculation of Maxwell’s Equations Using MATLAB

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH ◽

10.47191/ijmcr/v9i10.02 ◽

2021 ◽

Vol 09 (10) ◽

Author(s):

Subhi Abdalazim Aljily Osman ◽

Keyword(s):

Mathematical Method ◽

Analytical Solution ◽

Maxwell’S Equations ◽

Maxwell Equations ◽

Maxwell's Equations ◽

System Of Equations ◽

First Order ◽

Mathematical Programs ◽

Mathematical Problems ◽

Micro Radio

Maxwell’s equations describe electromagnetic Phenomena. This includes micro- , radio and radar waves .The Maxwell equations are discussed in more detail Faraday's and Amperes laws constitute a first - order hyperbolic system of equations .Matlab is one of the most famous mathematical programs in calculating mathematical problems .The aims of this study is to calculate Maxwell’s equations using Matlab .We followed the applied mathematical method by using Matlab .We found that the solution of Matlab is more accuracy and speed than the analytical solution.

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Plane wave ℋ (curl; Ω) conforming finite elements for Maxwell's equations

Computational Mechanics ◽

10.1007/s00466-003-0430-7 ◽

2003 ◽

Vol 31 (3) ◽

pp. 272-283 ◽

Cited By ~ 5

Author(s):

P. D. Ledger ◽

K. Morgan ◽

O. Hassan ◽

N. P. Weatherill

Keyword(s):

Finite Elements ◽

Plane Wave ◽

Maxwell’S Equations ◽

Maxwell's Equations

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Analytical Solution of System of Volterra Integral Equations Using OHAM

Journal of Mathematics ◽

10.1155/2020/8845491 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Muhammad Akbar ◽

Rashid Nawaz ◽

Sumbal Ahsan ◽

Dumitru Baleanu ◽

Kottakkaran Sooppy Nisar

Keyword(s):

Numerical Methods ◽

Analytical Solution ◽

Integral Equations ◽

Function Method ◽

Auxiliary Function ◽

Volterra Integral Equations ◽

Large Parameter ◽

Reliable Technique ◽

Present Technique ◽

Optimal Homotopy Asymptotic Method

In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.

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Maxwell fields satisfying Huygens's principle

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100043486 ◽

1968 ◽

Vol 64 (3) ◽

pp. 779-785 ◽

Cited By ~ 16

Author(s):

H. P. Künzle

Keyword(s):

Wave Equation ◽

Plane Wave ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Maxwell Fields ◽

Wave Space

AbstractIt is shown that Huygens's principle holds for the solutions of Maxwell's equations for p-forms of all degrees in a gravitational plane wave space, while the solutions of the wave equation for 1, 2, and 3-forms, however, may have tails.

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