| 高阶单步A-稳定指数拟合法 |
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| 引用本文： | 杨逢建,陈新明,罗毅平.高阶单步A-稳定指数拟合法[J].高校应用数学学报(英文版),1999,14(3):359-365. |
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| 作者姓名： | 杨逢建 陈新明 罗毅平 |
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| 作者单位： | [1]Dept.ofMath.,ZhongkaiAgrotechnicalCollege,Guangzhou510225. [4]Dept.ofMath.andPhys.,WuyiUnivezsity,Jiangmen,Guangdong529020. [5]Dept.ofBasis,XiangtanInstituteofMachineryandElectridty,Xiangtan411101. |
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| 摘 要： | In this paper,the necessary and sutlicient conditions for general one-step methoos to be exponentially fitted at q0∈C are given, A class of multtderivative hybrid one-step methods of order at least s 1 is constructed with s 1 parameters,where s is the order of derivative. The necessary and sufficient conditions for these methods to be A-stable and exponentially fitted is proved, Furthermore,a class of A-stable 2 parameters hybrid one-step methods of order at least 8 are constructed,which use 4th order derivative,These methods are exponentially fitted at q0 if and only its fitted function f(q) satisfies f(q0)= 0, Finally,an A-stable exponentlally fitted method of order 8 is obtained.
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| 关 键 词： | 高阶方程 拟合指数 稳定性 拟合函数 |
| 收稿时间： | 8 July 1998 |
High order one-step A-stable exponentially fitted methods |
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| Fengjian Yang,Xinming Chen,Yiping Luo.High order one-step A-stable exponentially fitted methods[J].Applied Mathematics A Journal of Chinese Universities,1999,14(3):359-365. |
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| Authors: | Fengjian Yang Xinming Chen Yiping Luo |
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| Institution: | (1) Dept. of Math., Zhongkai Agrotechnical College, 510225 Guangzhou;(2) Dept. of Math. and Phys., Wuyi University, 529020 Jiangmen, Guangdong;(3) Dept. of Basis, Xiangtan Institute of Machinery and Electricity, 411101 Xiangtan |
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| Abstract: | In this paper, the necessary and sufficient conditions for general one-step methods to be exponentially fitted at q
0∈C are given. A class of multiderivative hybrid one-step methods of order at least s+1 is constructed with s+1 parameters, where s is the order of derivative. The necessary and sufficient conditions for these methods to be A-stable and exponentially fitted
is proved. Furthermore, a class of A-stable 2 parameters hybrid one-step methods of order at least 8 are constructed, which
use 4th order derivative. These methods are exponentially fitted at q
0 if and only if its fitted function f(q) satisfies f(q
0)=0. Finally, an A-stable exponentially fitted method of order 8 is obtained. |
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| Keywords: | Multiderivative hybrid method exponentially fitted method A-stability |
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