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ERROR BOUNDS OF TRAPEZOIDAL RULE ON SUBINTERVALS USING DISTRIBUTION

  • Hong, Bum-Il ;
  • Hahm, Nahm-Woo
  • Received : 2007.03.22
  • Accepted : 2007.04.24
  • Published : 2007.06.25

Abstract

We showed in [2] that if $r\leq2$, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to $h^{2r+3}$ using zero mean Gaussian distribution under the assumption that we have subintervals (for simplicity equal length) partitioning and that each subinterval has the length. In this paper, if $r\geq3$, we show that zero mean Gaussian distribution of average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $Ch^8$.

Keywords

Trapezoidal rule;Error analysis;Wiener measure

References

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