| 二级对角隐Runge-Kutta方法的B-收敛性 |
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| 引用本文： | 左义君,张建国. 二级对角隐Runge-Kutta方法的B-收敛性[J]. 四川师范大学学报(自然科学版), 1991, 0(2) |
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| 作者姓名： | 左义君 张建国 |
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| 作者单位： | 四川师范大学数学系，四川师范大学数学系 |
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| 摘 要： | 本文讨论了二级对角隐 Runge-Kutta 方法的 B-相容,B-稳定及 B-收敛性,导出了方法的1阶最优 B-收敛性,从而改进和推广了朱方生1988年的结果.本文讨论 B-相容,B-稳定性所用方法不同于 Dekker & Verwer 1984年的方法,所得误差估计较前更为精确,其中 B-稳定性的讨论也推广和修正了 Burrage & Butcher 1979年的结果.
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| 关 键 词： | stiff非线性ODEs初值问题 二级对角隐R-K方法 B-相容性 B-稳定性 B-收敛性 |
B-CONVERGENCE OF THE TWO-STAGE DIAGONALLY IMPLICIT R-K METHODS |
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| Zuo Yijun,Zhang Jianguo. B-CONVERGENCE OF THE TWO-STAGE DIAGONALLY IMPLICIT R-K METHODS[J]. Journal of Sichuan Normal University(Natural Science), 1991, 0(2) |
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| Authors: | Zuo Yijun Zhang Jianguo |
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| Affiliation: | Zuo Yijun;Zhang Jianguo Department of Mathematics |
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| Abstract: | This paper explores B-consistency,B-stability and B-convergence of the two-stage diagonally implicit R-K methods,and the results improve and generalize those of Zhu Fangsheng(J.of Math.,PRC,1988).The technique used for discussions of the B-stability and B-consistency in this paper is different from that of Dekker & Verwer in 1984,the error bounds obained are sharper than those derived by them.The result about B-stability also generalizes and corrects that of Burrage & Butcher in 1979. |
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| Keywords: | Nonlinear stiff ODEs IVPs two-stage diagonally implicit R-K methods B-consistency B-stability B-convergence |
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