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Laplace Equation Inside a Cylinder: Computational Analysis and Asymptotic Behavior of the Solution

  • Suvra Sarkar
  • Sougata Patra
Conference paper
  • 1.1k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)

Abstract

The Laplacian in the cylindrical coordinate space has been considered to approximate the solution of a conservative field within a restricted domain.

$$ {{\partial^{2}\psi} \over {\partial\rho^2}} + {{1\delta\psi} \over {\rho\partial\rho}} + {{1} \over {\rho^2}}{ {\partial^{2}\psi} \over {\partial\phi^2}} +{{\partial^{2}\psi} \over {\partial{z}^2} } =0 $$

Solutions of the Laplacian are represented by expansion in series of the appropriate orthonormal functions. By using asymptotic relations of Bessel Series and Fourier Bessel series, we establish some criteria for the solution to properly reflect the nature of the conservative field.

Keywords

Bessel functions Fourier-Bessel Series Kronecker Delta Laplace Equation 

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References

  1. 1.
    Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1975)zbMATHGoogle Scholar
  2. 2.
    Watson, G.N.: A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge (1944)zbMATHGoogle Scholar
  3. 3.
    Lighthill, M.J.: Fourier analysis and Generalized Functions. Cambridge University Press, Cambridge (1975)Google Scholar
  4. 4.
    Partial Differential Equation Toolbox Users Guide, The MathWorks, http://www.mathworks.com/access/helpdesk/help/toolbox/pde/pde.shtml

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Suvra Sarkar
    • 1
  • Sougata Patra
    • 1
  1. 1.Department of Electronics and Communication EngineeringHaldia Institute of Technology, Indian Centre for Advancement in Research and EducationHaldia 

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