NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan
53rd NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan
Session ID : 2D9
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OS20-2
Numerical Computations of Picard's Formula
*Hiroshi FUJIWARA
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Abstract
We show a new approach to numerical reconstruction of the solution ofan integral equation of the first kind.In usual the collocation methods or Galerkin methods are used for suchpurpose, however, instability caused by ill-posedness of integralequations of the first kind prevents us from processing numerical schemes.We propose the use of Picard's formula which gives the exact solutionof an integral equation with its singular system.Though finding the singular system was often hard both exactly andnumerically, multiple-precision arithmetic and a high-accuratenumerical integration formula has been proposed to constructthe singular system in recent research.This leads us to the numerical realization of Picard's formula.
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© 2004 Committee for Mechanics and Structure,Science Council
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