| 一类解刚性微分方程的Adams型混杂法 |
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| 引用本文： | 范晓燕,张国凤. 一类解刚性微分方程的Adams型混杂法[J]. 兰州大学学报(自然科学版), 2005, 41(6): 134-137 |
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| 作者姓名： | 范晓燕 张国凤 |
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| 作者单位： | 西北师范大学,数学与信息科学学院,甘肃,兰州,730070;兰州大学数学与统计学院,甘肃,兰州,730000 |
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| 摘 要： | 构造了一类带参数的k步k 2阶的Adams型混杂法,讨论了该方法的稳定性质并证明了该方法与一类改进的二阶导数法等价.在实现Newton迭代计算时,该方法要优于改进的二阶导数法,因此对于求解Stiff问题,这类方法具有一定的优势.最后给出了数值实例.
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| 关 键 词： | 混杂法 Stiff稳定 A-稳定 |
| 文章编号： | 0455-2059（2005）06-0134-04 |
| 收稿时间： | 2004-03-03 |
| 修稿时间： | 2004-03-03 |
A class of Adams hybrid methods for solving problems of stiff ODEs |
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| FAN Xiao-yan,ZHANG Guo-feng. A class of Adams hybrid methods for solving problems of stiff ODEs[J]. Journal of Lanzhou University(Natural Science), 2005, 41(6): 134-137 |
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| Authors: | FAN Xiao-yan ZHANG Guo-feng |
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| Affiliation: | 1.College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730000, China; 2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China |
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| Abstract: | A class of k-step, (k+2) order hybrid methods for solving problems of stiff ODEs are constructed and its stability properties are discussed. The method is proved to be equal to a class of improved second derivative multistep methods. Implementated by Newton iteration, our methods are more efficient for solving non-linear stiff problems. Finally, some numerical results are presented. |
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| Keywords: | hybrid method stiff problem A-stability |
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