梯形修正公式及其余项“中间点”的渐近性

Modified Formula for Trapezoid Method and the Asymptotic Property of the"Mid-point"of Its Remainder

给出了一种带端点导数的梯形修正公式,并给出了该公式的截断误差。分析了相应的复化求积公式的收敛阶,其收敛阶比复化梯形法提高了2阶;并通过对梯形修正公式余项的研究。讨论了该求积公式余项"中间点"的渐近性,使求积公式的代数精度得到进一步提高。

A modified formula for trapezoid method and its truncation error are presented. The convergence order of its compound formula is analyzed. There are 2 more ranks of the convergence order in this modified formula. The asymptotic property of the ＂mid-point＂ of the remainder of modified formula for trapezoid method is discussed by studying the remainder formula. The algebraic accuracy of the integration formula is more improved.