| 方程x′(t)=ax(t)+bx([t])数值解的振动性(英文) |
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| 引用本文： | 王琦,温洁嫦. 方程x′(t)=ax(t)+bx([t])数值解的振动性(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： | 王琦 温洁嫦 |
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| 摘 要： | 将θ-方法用于求解一类自变量分段连续型延迟微分方程,研究数值解的振动性以及数值方法对方程本身振动性的保持性质。通过对差分方程的分析,得到数值解在一般节点与整数节点处振动与非振动的等价性,进而获得了θ-方法的振动性条件,证明解析解的振动性能够被θ-方法保持。最后讨论了稳定性与振动性之间的关系。
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| 关 键 词： | 数值解 θ-方法 振动性 |
Oscillation of numerical solution for equation x'(t) =ax(t) +bx([t]) |
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| WANG Qi,WEN Jie-chang. Oscillation of numerical solution for equation x'(t) =ax(t) +bx([t])[J]. Journal of Natural Science of Heilongjiang University, 2010, 27(5) |
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| Authors: | WANG Qi WEN Jie-chang |
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| Abstract: | Applying θ-methods to a class of the differential equations with piecewise constant arguments , the oscillation and the preservation of oscillation of numerical solution are studied. The equivalence of the oscillation and non-oscillation between the integer nodes and the any nodes are obtained by analyzing the difference equation. Furthermore, the conditions of oscillation for the θ-methods are given. It is proven that the oscillation of analytic solution can be preserved by the θ-methods. Finally, the relationship between stability and oscillation are discussed. |
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| Keywords: | numerical solution θ-methods oscillation |
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