| 分段连续微分方程θ-方法的稳定性(英文) |
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| 引用本文： | 张如,徐阳. 分段连续微分方程θ-方法的稳定性(英文)[J]. 黑龙江大学自然科学学报, 2010, 27(5) |
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| 作者姓名： | 张如 徐阳 |
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| 基金项目： | Natural Science Foundation of Heilongjiang Province，the Science Research Foundation，the Natural Scientific Research Innovation Foundation |
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| 摘 要： | 讨论分段连续型微分方程x′(t)=ax(t)+a1x([t+3])的解析解的稳定性,得出其渐进稳定的一个充分必要条件。应用θ-方法求解此分段连续型微分方程,得到相应的数值稳定区域,给出数值解的稳定区域包含解析解的稳定区域的一个充分必要条件。应用线性θ-方法求解了微分方程x′(t)=ax(t)+a1x([t+p]),给出此类数值方法渐进稳定的一个充分条件,得出数值解的稳定区域包含解析解的稳定区域的充分条件。
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| 关 键 词： | 分段连续微分方程 θ-方法 稳定性 |
The differential equation with piecewise continuous arguments |
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| ZHANG Ru,XU Yang. The differential equation with piecewise continuous arguments[J]. Journal of Natural Science of Heilongjiang University, 2010, 27(5) |
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| Authors: | ZHANG Ru XU Yang |
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| Abstract: | The stability of the analytic solution of the differential equation x'(t)= ax(t)+a1x([t+3])with piecewise continuous arguments is considered.The conditions of asymptotic stability for the e-quation are obtained.Moreover,θ-methods are applied to this kind of equations,and the stability re-gion of θ-method is obtained.A necessary and sufficient condition under which the analytic stability re-gion is contained in the numerical stability region is also obtained.Then,apply the linear θ-method to the equation x'(t)= ax(t)+a1x([t+p]),a sufficient condition of the asymptotic stability is investiga-ted,and a sufficient condition is obtained under which the analytic stability region is contained in the nu-merical stability region. |
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| Keywords: | delay differential equations with piecewise continuous arguments θ-method stability |
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