带导数的自适应变阶积分公式

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。

Adaptive changeable Order Formula with Derivatives

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 al...