Numerical Inversion Technique for the One and Two-Dimen- sional $mathcal{L}_2$-Transform Using the Fourier Series and Its Application to Fractional Partial Differential Equations

Arman Aghili; Alireza Ansari

Original Article

Kyungpook Mathematical Journal 2012; 52(4): 383-395

Published online December 23, 2012

Numerical Inversion Technique for the One and Two-Dimen- sional $mathcal{L}_2$-Transform Using the Fourier Series and Its Application to Fractional Partial Differential Equations

Arman Aghili¹, Alireza Ansari²

¹Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 1914, Rasht, Iran
²Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran

Received: December 23, 2012; Revised: December 23, 2012; Accepted: December 23, 2012

Abstract

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Abstract

In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.

Keywords: Laplace transform, $mathcal{L}_2$-transform, Fourier series, Numerical inversion method.