Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods
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For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree \(\le r - 1.\) We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4r in the interpolation at Gauss points can be improved to \(4r+2\). We illustrate the improvement of the order of convergence by numerical experiments.
KeywordsExtrapolation Integral equation Interpolation Gauss points
Mathematics Subject Classification45B05 (Fredholm integral equation)
- 7.Chandler, G.A.: Superconvergence of numerical solutions of second kind integral equations. PhD thesis, Australian National University (1979)Google Scholar