Communications of the
Korean Mathematical Society CKMS

We computed zero mean Gaussian of average error bounds of Simpson's quadrature with covariances in [2]. In this paper, we compute zero mean Gaussian of average error bounds between Simpson's quadrature and composite Simpson's quadrature on four consecutive subintervals. The reason why we compute these on subintervals is because these results enable us to compute {\it a posteriori} error bounds on the whole interval in the later paper.

Keywords: Simpson's quadrature, error analysis, Wiener measure

MSC numbers: 65D30, 65G10, 28C20