ERROR BOUNDS OF TRAPEZOIDAL RULE ON SUBINTERVALS USING DISTRIBUTION

Abstract

We showed in [2] that if <TEX>$r\leq2$</TEX>, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to <TEX>$h^{2r+3}$</TEX> 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 <TEX>$r\geq3$</TEX>, 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 <TEX>$Ch^8$</TEX>.