Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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NUMERICAL EXPERIMENTS OF THE LEGENDRE POLYNOMIAL BY GENERALIZED DIFFERENTIAL TRANSFORM METHOD FOR SOLVING THE LAPLACE EQUATION

  • Amoupour, Ebrahim (Department of Electronic Engineer Roudsar and Amlash Branch Islamic Azad University) ;
  • Toroqi, Elyas Arsanjani (Department of Applied Mathematics Faculty of Mathematics Lahijan Branch Islamic Azad University) ;
  • Najafi, Hashem Saberi (Department of Applied Mathematics Faculty of Mathematics Lahijan Branch Islamic Azad University)
  • Received : 2017.05.13
  • Accepted : 2018.03.01
  • Published : 2018.04.30
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Abstract

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.

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References

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