随机变延迟微分方程平衡方法的均方收敛性与稳定性
MEAN SQUARE CONVERGENCE AND STABILITY OF BALANCED METHODS FOR STOCHASTIC VARIABLE DELAY DIFFERENTIAL EQUATIONS
查看参考文献14篇
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文摘
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针对一类变延迟微分方程,应用全隐式方法一平衡方法,研究了其收敛性和稳定性.结果表明平衡方法以$\frac{1}{2}\gamma,\gamma \in \left( {0,1} \right]$阶收敛到精确解;并且强平衡方法和弱平衡方法都能保持解析解的均方稳定性;进一步数值实验验证了算法理论分析的正确性,并且表明全隐式的平衡方法比显式方法- Euler方法具有更好的稳定性. |
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其他语种文摘
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The convergence and stability of a class of variable delay differential equations are studied by using a fully implicit method balanced methods. The results show that the balanced methods converges to the exact solution of order $\frac{1}{2}\gamma,\gamma \in \left( {0,1} \right]$; Moreover, both the strong balanced methods and the weak balanced methods can reproduce the mean-square stability of the system with sufficiently small stepsize h; Further, some numerical experiments included in the paper illustrate the theoretical results, and show that the fully implicit balanced methods has better stability than the explicit — Euler methods. |
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来源
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计算数学
,2021,43(3):301-321 【核心库】
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DOI
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10.12286/jssx.j2019-0610
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关键词
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随机变延迟微分方程
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平衡方法
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均方收敛性
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均方稳定性
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地址
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江西理工大学理学院, 赣州, 341000
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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基金
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国家自然科学基金
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江西省教育厅青年资金项目
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江西理工大学创新创业训练计划项目
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文献收藏号
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CSCD:7118702
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