Research ArticleOpen AccessGoogle Scholar indexed
Laplace Transform Analytical Restructure
Department of Mathematics, Faculty of Basic Education, PAAET, Shaamyia, Kuwait
M. S. Software Engg, SITE, V. I. T. University, Vellore, India
- 1 Department of Mathematics, Faculty of Basic Education, PAAET, Shaamyia, Kuwait
- 2 M. S. Software Engg, SITE, V. I. T. University, Vellore, India
Copy link · social · email
Abstract
In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation of the original function. Various analytic consequent results are given. The simplicity and efficacy of the method are illustrated through many examples with shown Maple graphs, and transform tables are provided. Finally, a new infinite series representation related to Laplace transforms of trigonometric functions is proposed.
KeywordsLaplace TransformNatural TransformSumudu Transform
- L. Debnath and D. Bhatta, “Integral Transforms and Their Applications,” 2nd Edition, C. R. C. Press, London, 2007.
- P. P. G. Dyke, “An Introduction to Laplace Transform and Fourier Series,” Springer-Verlag, London, 2004.
- A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, “Tables of Integral transform,” Vol. 1, McGrawHill, New York, Toronto, London, 1954.
- M. Rahman, “Integral Equations and Their Applications,” WIT Press, Boston, 2007.
- J. L. Schiff, “Laplace Transform Theory and Applications,” Springer, Auckland, 2005.
- M. R. Spiegel, “Theory and Problems of Laplace Transforms,” Schaums Outline Series, McGraw-Hill, New York, 1965.
- W. T. Thomson, “Laplace Transformation Theory and Engineering Applications,” Prentice-Hall Engg Design Series, Printice-Hall Inc., New York, 1950.
- D. V. Widder, “The Laplace Transform,” Oxford University Press, London, 1946.
- F. B. M. Belgacem, A. A. Karaballi and S. L. Kalla, “Analytical Investigations of the Sumudu Transform and Applications to Integral Production Equations,” Mathematical Problems in Engineering (MPE), Vol. 2003, No. 3, 2003, pp. 103-118.
- F. B. M. Belgacem and A. A. Karaballi, “Sumudu Transform Fundamental Properties Investigations and Applications,” Journal of Applied Mathematics and Stochastic Analysis (JAMSA), 2005, Article ID: 91083.
- F. B. M. Belgacem, “Introducing and Analysing Deeper Sumudu Properties,” Nonlinear Studies Journal (NSJ), Vol. 13, No. 1, 2006, pp. 23-41.
- F. B. M. Belgacem, “Applications of Sumudu Transform to Indefinite Periodic Parabolic Equations,” In: Proceedings of the 6th International Conference on Mathematical Problems & Aerospace Sciences (ICNPAA 06), Chap. 6, Cambridge Scientific Publishers, Cambridge, 2007, pp 51-60.
- F. B. M. Belgacem, “Sumudu Applications to Maxwell’s Equations,” PIERS Online, Vol. 5, No. 4, 2009, pp 355360. doi:10.2529/PIERS090120050621
- F. B. M. Belgacem, “Sumudu Transform Applications to Bessel’s Functions and Equations,” Applied Mathematical Sciences, Vol. 4, No. 74, 2010, pp. 3665-3686.
- M. G. M. Hussain and F. B. M. Belgacem, “Transient Solutions of Maxwell’s Equations Based on Sumudu Transform,” Journal of Progress in Electromagnetics Research (PIER), Vol. 74, 2007, pp. 273-289. doi:10.2528/PIER07050904