两类线性泛函微分方程数值解的振动性分析  

OSCILLATION ANALYSIS OF NUMERICAL SOLUTIONS FOR TWO KINDS OF LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

作　　者：王云竹[1] 高建芳[1] 

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025

出　　处：《高等学校计算数学学报》2017年第2期97-107,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：黑龙江省自然科学基金(A201411);黑龙江省自然科学基金(F2015012);国家自然科学基金(11401145)

摘　　要：1引言近些年来泛函微分方程(FDEs)解析解的振动性得到了广泛的关注,如文献[1,2,3,4,5,6,7,8,9,10,11],这是因为在生物、医学等领域中都出现了与其相关的数学模型[12,13,14].但是关于泛函微分方程数值解振动性的研究却很少,文献[15,16]分别研究了造血模型和种群动力学模型的数值解的振动性,文献[17,18,19。The paper considers the oscillation of numerical solutions for two kinds of linear functional differential equations by the P-method. Through the oscillatory equivalence, the advanced functional differential equation is transformed into the delay functional differential equation. By judging the roots of the characteristic equation, some conditions under which the numerical solution is oscillatory are obtained and it is proved that the oscillations of the analytic solutions are preserved by the numerical solutions under some conditions. Besides, for the special case of P-method, the trapezoidal method, it is proved that the trapezoidal method can keep the oscillation property of the analytic solution without any condition. In the end, the article gives numerical experiments.

关 键 词：functional differential equation numerical solutions OSCILLATION 

分 类 号：O241.81[理学—计算数学]