Laplace Transform Analytical Restructure

Affiliation(s)

Department of Mathematics, Faculty of Basic Education, PAAET, Shaamyia, Kuwait.

M. S. Software Engg, SITE, V. I. T. University, Vellore, India.

Department of Mathematics, Faculty of Basic Education, PAAET, Shaamyia, Kuwait.

M. S. Software Engg, SITE, V. I. T. University, Vellore, India.

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.

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.

Cite this paper

F. Belgacem and R. Silambarasan, "Laplace Transform Analytical Restructure,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 919-932. doi: 10.4236/am.2013.46128.

F. Belgacem and R. Silambarasan, "Laplace Transform Analytical Restructure,"

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