带导数的自适应变阶积分公式  

Adaptive Changeable Order Formula with Derivatives

作　　者：杨录峰[1] 徐峰[1] 

机构地区：[1]北方民族大学信息与计算科学学院,银川750021

出　　处：《科学技术与工程》2010年第12期2822-2824,共3页Science Technology and Engineering

基　　金：国家自然科学基金项目(10671157);北方民族大学科研项目(2008Y032)资助

摘　　要：利用自适应Simpson算法和基于Hermite插值导出的带端点导数的Romberg外推算法结合思想,提出一种新型的带端点导数的自适应变阶积分公式:它兼有变步长计算和逐步提高数值积分法收敛阶的优点。数值算例表明,当被积函数在积分区间上变化性态急剧多变时,与自适应Simpson算法和Romberg外推算法相比,新算法的求解精度有了较大提高。当精度要求一定时,新算法大大减少了计算量。By means of adaptive Simpson algorithm and Romberg algorithm with extreme point derivatives, a new type of adaptive numerical quadrature algorithm with derivatives is presented, which takes the advantage of both the step-changeable computation and the convergence order of numerical quadrature be improved step by step Numerical examples show that all the results of the improved solution are more accurate. For a given accuracy, the new algorithm needs fewer computations, compared with the adaptive Simpson algorithm and the Romberg extrapolation algorithm.

关 键 词：自适应Simpson算法 Hermite公式 Romberg算法 变阶公式 

分 类 号：O241.4[理学—计算数学]