| Heun方法中用Simpson公式校正的改进 |
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| 引用本文： | 张顺,李志远.Heun方法中用Simpson公式校正的改进[J].合肥学院学报(自然科学版),2010,20(1):8-11. |
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| 作者姓名： | 张顺 李志远 |
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| 作者单位： | 1. 安徽大学,计算机科学与技术学院,合肥,230039
2. 中国科学技术大学,数学系,合肥,230026 |
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| 基金项目： | 安徽省自然科学基金项目 |
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| 摘 要： | 针对求解常微分方程初值问题的Heun方法,利用Simpson公式进行校正,其中采用二次Taylor级数展开,改进了数值近似解的精度,并进行了实例说明.
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| 关 键 词： | 初值问题 Heun方法 梯形公式 Simpson公式 |
Improved Correction by Simpson's Rule in Heun's Method |
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| ZHANG Shun,LI Zhi-yuan.Improved Correction by Simpson''s Rule in Heun''s Method[J].Journal of Hefei University :Natural Sciences,2010,20(1):8-11. |
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| Authors: | ZHANG Shun LI Zhi-yuan |
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| Institution: | 1. School of Compnter Science and Technology, Anhui University, Hefei 230039 ;2. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China) |
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| Abstract: | Based on Heun＇s method, We apply a Taylor series expansion of order two, use Simpson＇s rule to make a correction, and obtain final numerical approximate solutions of the initial value problem of ordinary differential equations. The method improves the precision of numerical approximations of original Heun＇s method. Moreover, a typical example is given for more sufficient explanations. |
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| Keywords: | initial value problem Heun＇s method trapezoidal rule Simpson＇s rule |
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