安徽大学学报（自然科学版）
安徽大學學報（自然科學版）
안휘대학학보（자연과학판）
JOURNAL OF ANHUI UNIVERSITY(NATURAL SCIENCES EDITION)
2011年
1期
15-20
,共6页
振动性%稳定性%θ-方法%向前型%分段连续项
振動性%穩定性%θ-方法%嚮前型%分段連續項
진동성%은정성%θ-방법%향전형%분단련속항
oscillation%stability%θ-methods%advanced type%piecewise constant arguments
将两种θ-方法:线性θ-方法和单腿θ-方法用于求解一类自变量分段连续向前型微分方程,通过对差分格式进行分析,得到了一般节点与整数节点处非振动的等价性,进而获得了θ-方法振动的条件.证明了θ-方法能够保持解析解的振动性,进一步分析了稳定性与振动性的关系,最后给出几个数值例子.
將兩種θ-方法:線性θ-方法和單腿θ-方法用于求解一類自變量分段連續嚮前型微分方程,通過對差分格式進行分析,得到瞭一般節點與整數節點處非振動的等價性,進而穫得瞭θ-方法振動的條件.證明瞭θ-方法能夠保持解析解的振動性,進一步分析瞭穩定性與振動性的關繫,最後給齣幾箇數值例子.
장량충θ-방법:선성θ-방법화단퇴θ-방법용우구해일류자변량분단련속향전형미분방정,통과대차분격식진행분석,득도료일반절점여정수절점처비진동적등개성,진이획득료θ-방법진동적조건.증명료θ-방법능구보지해석해적진동성,진일보분석료은정성여진동성적관계,최후급출궤개수치례자.
Applying two θ-methods, namely the linear θ-method and one-leg θ-method to the differential equations with piecewise constant arguments of advanced type. The equivalence of the non-oscillation between the integer nodes and the any nodes were obtained by analyzing the difference form. Moreover, the conditions of oscillation for the θ-methods were given. It wag proved that the θ-methods preserved the oscillation of analytic solution. In addition, the relationship between stability and oscillation were investigated. Finally, several numerical examples were given.
