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A Two-Grid Method for a Second Kind Integral Equation with Green’s Kernel

In: Integral Methods in Science and Engineering, Volume 2

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  • R. P. Kulkarni

    (Indian Institute of Technology, Powai)

Abstract

In this chapter we consider two-grid methods for the second kind integral equation with Green’s kernel. Two-grid methods based on the Nyström operator have been studied in [At97], whereas methods based on a new approximating operator have been defined in [Ku04]. In the case of an integral operator with Green’s kernel, the usual definition of the Nyström operator by replacing the integration with a numerical quadrature results in a loss of accuracy. Whereas in [AtSh07] a modified Nyström operator is defined explicitly, a similar treatment is considered in [Ku05]. The purpose of this chapter is to define two-grid methods based on the modified Nyström operator. We compare the performance of these methods by a concrete example.

Suggested Citation

  • R. P. Kulkarni, 2010. "A Two-Grid Method for a Second Kind Integral Equation with Green’s Kernel," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 2, chapter 24, pages 253-260, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4897-8_24
    DOI: 10.1007/978-0-8176-4897-8_24
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