【摘要】 本文基于不等距牛顿插值,简捷地导出了一个新的积分公式及其截断误差。新的算法比Gear、BDF、PBD方法稳定、有效,它的积分步数、牛顿迭代次数及Jacob修改次数均可明显减少。文中还讨论了自开始、自动变阶变步长、输出点插值以及程序组织方法,并用计算实例对算法的效果进行了检验。更多还原

【Abstract】 A new integration formula and its local truncation error are presented on the basis of non-iso-interval Newton interpolation. The new integration algorithm appears to be more stable and efficient than the methods of Gear, BDF, PBD. Its numbers of the integration steps, Newton iterations, Jacob modifications may be decreased significantly. The self-start, automatic variating order and step of the integration, the interpolation of output points and the structure of the integration program are discussed and the effect of the algorithm is assessed by using numerical caculations.更多还原