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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.
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참고문헌 (23)
참고문헌 신청
A. V. Bakshi / 2008 / Electromagnetic Theory / Technical publications Pune
D. R. Bland / 1961 / Solutions of Laplace's Equation / Routledge and Keegan Paul Ltd.
V. S. Erturk / 2008 / Application of generalized differential transform method to multi-order fractional differential equations / Commun. Nonlinear Sci. Numer. Simul. 13(8):1642~1654
E. Fehlberg / 1968 / Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Step Size Control / George C. Marshal space flight center
E. Fehlberg / 1970 / Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Warmeleitungsprobleme / Computing (Arch. Elektron. Rechnen) 6:61~71
D. R. Bland / 1961 / Solutions of Laplace's Equation / Routledge and Keegan Paul Ltd.
V. S. Erturk / 2008 / Application of generalized differential transform method to multi-order fractional differential equations / Commun. Nonlinear Sci. Numer. Simul. 13(8):1642~1654
E. Fehlberg / 1968 / Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Step Size Control / George C. Marshal space flight center
E. Fehlberg / 1970 / Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Warmeleitungsprobleme / Computing (Arch. Elektron. Rechnen) 6:61~71
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