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| 一种变步长和变阶计算的自适应数值积分算法 | |
| 引用本文： | 杨录峰,马宁,赵双锁. 一种变步长和变阶计算的自适应数值积分算法[J]. 云南民族大学学报(自然科学版), 2011, 20(1): 32-36,41. DOI: 10.3969/j.issn.1672-8513.2011.01.008 |
| 作者姓名： | 杨录峰 马宁 赵双锁 |
| 作者单位： | 1. 北方民族大学,信息与计算科学学院,宁夏,银川,750021 2. 吴忠市气象局,宁夏,吴忠,751300 3. 北方民族大学,信息与计算科学学院,宁夏,银川,750021;兰州大学,数学与统计学院,甘肃,兰州,730001 |
| 基金项目： | 国家自然科学基金，国家民委科研项目，北方民族大学科研项目 |
| 摘 要： | 将自适应Simpson算法和Romberg外推算法相结合,提出一种新型的自适应S-R(Simpson-Romberg)算法,它兼有变步长计算和逐步提高数值积分法收敛阶的优点.若干数值比较算例表明,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,它具有明显优势. |
| 关 键 词： | 数值积分法 自适应Simpson算法 Romberg外推算法 自适应S-R算法 |
An Adaptive Numerical Quadrature Algorithem of Computing with Both Changeable Step and Changeable Order |
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| YANG Lu-feng,MA Ning,ZHAO Shuang-suo. An Adaptive Numerical Quadrature Algorithem of Computing with Both Changeable Step and Changeable Order[J]. Journal of Yunnan Nationalities University:Natural Sciences Edition, 2011, 20(1): 32-36,41. DOI: 10.3969/j.issn.1672-8513.2011.01.008 | |
| Authors: | YANG Lu-feng MA Ning ZHAO Shuang-suo |
| Affiliation: | YANG Lu-feng1,MA Ning2,ZHAO Shuang-suo1,3(1.Institute of Information and Computation Science,Beifang University of Nationalties,Yinchan 750021,China,2.Wuzhong Meteorological Bureau,Wuzhong 751300,3.Institute of Mathematics and Statistics,Lanzhou University,Lanzhou 730001,China) |
| Abstract: | Adaptive S-R(simpson-romberg) Algorithm,a new type of adaptive numerical quadrature algorithm,is presented,which combines the adaptive Simpson algorithm with Romberg extrapolation algorithm.It possesses both the merits of the step-changeable computation and those of the gradual convergence order of numerical quadrature.The comparison of several numerical examples has indicated that the adaptive S-R algorithm has obvious superiority compared with the adaptive Simpson algorithm and the Romberg extrapolation a... |
| Keywords: | numerical integration adaptive simpson algorithm romberg extrapolation algorithm adaptive S-R algorithm |
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