# A STUDY OF AVERAGE ERROR BOUND OF TRAPEZOIDAL RULE

• Yang, Mee-Hyea (Department of Mathematics, The University of Incheon) ;
• Hong, Bum-Il (Department of Mathematics, Kyung Hee University)
• Published : 2008.09.25
• 66 1

#### Abstract

In this paper, to have a better a posteriori error bound of the average case error between the true value of I(f) and the Trapezoidal rule on subintervals using zero mean-Gaussian, we prove that a new average error between the difference of the true value of I(f) from the composite Trapezoidal rule and that of the composite Trapezoidal rule from the simple Trapezoidal rule is bounded by $c_rH^{2r+3}$ through direct computation of constants $c_r$ for r ${\leq}$ 2 under the assumption that we have subintervals (for simplicity equal length h) partitioning [0, 1].

#### Keywords

Trapezoidal rule;Error analysis;Wiener measure

#### References

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#### Cited by

1. ON A STUDY OF ERROR BOUNDS OF TRAPEZOIDAL RULE vol.36, pp.2, 2014, https://doi.org/10.5831/HMJ.2014.36.2.291