Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2018; 33(2): 639-650

Printed April 30, 2018

https://doi.org/10.4134/CKMS.c170202

Copyright © The Korean Mathematical Society.

Numerical experiments of the Legendre polynomial by generalized differential transform method for solving the Laplace equation

Ebrahim Amoupour, Elyas Arsanjani Toroqi, Hashem Saberi Najafi

Roudsar and Amlash Branch Islamic Azad University, Lahijan Branch Islamic Azad University, Lahijan Branch Islamic Azad University

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Finding a solution for the Legendre equation is difficult. Especially if it is as a part of the Laplace equation solving in the electric fields. In this paper, first a problem of the generalized differential transform method (GDTM) is solved by the Sturm-Liouville equation, then the Legendre equation is solved by using it. To continue, the approximate solution is compared with the nth-degree Legendre polynomial for obtaining the inner and outer potential of a sphere. This approximate is more accurate than the previous solutions, and is closer to an ideal potential in the intervals.

Keywords: generalized differential transform method, Legendre polynomial, Sturm-Lioville equation

MSC numbers: 35J05, 35C10, 26A33

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