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

作　　者：何俊红[1] 

机构地区：[1]宝鸡文理学院数学系,宝鸡721007

出　　处：《科学技术与工程》2010年第8期1936-1939,共4页Science Technology and Engineering

基　　金：宝鸡文理学院院级重点项目(ZK2309)资助

摘　　要：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.

关 键 词：梯形修正公式 截断误差 收敛阶 渐近性 

分 类 号：O241.4[理学—计算数学]