The Mathematical Institute, University of Oxford, Eprints Archive

Efficient high-order rational integration and deferred correction with equispaced data

Guettel, Stefan and Klein, Georges (2013) Efficient high-order rational integration and deferred correction with equispaced data. Technical Report. Unspecified. (Submitted)



Stable high-order linear interpolation schemes are well suited for the accurate approximation of antiderivatives and the construction of efficient quadrature rules. In this paper we utilize for this purpose the family of linear barycentric rational interpolants by Floater and Hormann, which are particularly useful for interpolation with equispaced nodes. We analyze the convergence of integrals of these interpolants to those of analytic functions as well as functions with a finite number of continuous derivatives. As a by-product, our convergence analysis leads to an extrapolation scheme for rational quadrature at equispaced nodes. Furthermore, as a main application of our analysis, we present and investigate a new iterated deferred correction method for the solution of initial value problems, which allows to work efficiently even with large numbers of equispaced data. This so-called rational deferred correction (RDC) method turns out to be highly competitive with other methods relying on more involved implementations or non-equispaced node distributions. Extensive numerical experiments are carried out, comparing the RDC method to the well established spectral deferred correction (SDC) method by Dutt, Greengard and Rokhlin.

Item Type:Technical Report (Technical Report)
Subjects:A - C > Approximations and expansions
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1708
Deposited By: Lotti Ekert
Deposited On:26 Jun 2013 08:13
Last Modified:29 May 2015 19:24

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