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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 74 > pp. 273-289
## TRANSIENT SOLUTIONS OF MAXWELL'S EQUATIONS BASED ON SUMUDU TRANSFORMBy M. G. M. Hussain and F. B. M. M. Belgacern
Abstract:
The Sumudu transform is derived from the classical Fourier integral. Based on the mathematical simplicity of the Sumudu transform and its fundamental properties, Maxwell's equations are solved for transient electromagnetic waves propagating in lossy conducting media. The Sumudu transform of Maxwell's differential equations yields a solution directly in the time domain, which neutralizes the need to perform inverse Sumudu transform. Two sets of computer plots are generated for the solution of Maxwell's equations for transient electric field strength in lossy medium. A set of plots presents the Sumudu transform of the transient solution and another one presents inverse Sumudu transform. Both sets of plots reveal similar characteristics and convey equal information. Such property is referred to as the Sumudu reciprocity.
2. Watugala, G. K., "Sumudu transform a new integral transform to solve differential equations and control engineering problems," 3. Belgacem, F. B. M., 4. Belgacem, F. B. M., "Introducing and analysing deeper Sumudu properties," 5. Belgacem, F. B. M. and A. A. Karaballi, "Sumudu transform fundamental properties investigations and applications," 6. Belgacem, F. B. M., A. A Karaballi, and L. S. Kalla, "Analytical investigations of the Sumudu transform, and applications to integral production equations," 7. Asiru, M. A., "Sumudu transform and solution of integral equations of convolution type," 8. Asiru, M. A., "Further properties of the Sumudu transform and its applications," 9. Asiru, M. A., "Applications of the Sumudu transform to discrete dynamicsystem," 10. Weerakoon, S., "Application of Sumudu transform to partial differential equations," 11. Weerakoon, S., "Complex inversion formula for Sumudu transform," 12. Stratton, J. A., 13. Kong, J. A., 14. Harmuth, H. F. and M. G. M. Hussain, 15. Zhou, X., "On independence, completeness of Maxwell's equations and uniqueness theorems in electromagnetics," 16. Hussain, M. G. M., "Mathematical model for the electromagnetic conductivity of lossy materials," 17. Shen, J., "Time harmonic electromagnetic fields in an biaxial anisotropic medium," 18. El-Shandwily, M. E., "Solutions of Maxwell's equations for general nonperiodic waves in lossy media," 19. Thomson, W. T., 20. Watugala, G. K., "Sumudu transform for functions of two variables," |

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