删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

中立型比例延迟微分系统线性θ-方法的渐近估计

本站小编 Free考研考试/2021-12-27

张根根1, 肖爱国1, 王晚生2
1 湘潭大学数学与计算科学学院, 湘潭 411105;
2 上海师范大学数理学院, 上海 200234
收稿日期:2018-11-01出版日期:2020-11-15发布日期:2020-11-15


基金资助:国家自然科学基金(11671343,11771060,11701110)资助.


THE ASYMPTOTIC ESTIMATE OF LINEAR θ-METHODS FOR SYSTEM OF NEUTRAL PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS

Zhang Gengen1, Xiao Aiguo1, Wang Wansheng2
1 School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China;
2 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Received:2018-11-01Online:2020-11-15Published:2020-11-15







摘要



编辑推荐
-->


本文研究了一类线性非自治中立型比例延迟微分系统线性θ-方法的渐近稳定性,并借助于泛函不等式得到了数值解的渐近估计.此渐近估计不仅比数值渐近稳定性描述得更加精确,而且还能给出非稳定情形数值解的上界估计式.数值算例验证了相关理论结果.
MR(2010)主题分类:
65L05
65L20
34K28
34K40

分享此文:
θ-方法的渐近估计”的文章,特向您推荐。请打开下面的网址:http://www.computmath.com/jssx/CN/abstract/abstract74.shtml' name="neirong">θ-方法的渐近估计'>

()

[1] Bellen A, Gugllelmi N, Zennaro M. On the contractivity and asymptotic stability of systems of delay differential equations of neutral type[J]. BIT Numer. Math., 1999, 39(1):1-24.

[2] Bellen A, Zennaro M. Numerical Methods for Delay Differential Equations[M]. Oxford University Press, 2003.

[3] Buhmann M, Iserles A. Staility of the discretized pantograph differential equation[J]. Math. Comput., 1993, 60(202):575-589.

[4] ?ermák J. The asymptotic of solutions for a class of delay differential equations[J]. Rocky Mountain J. Math., 2003, 33:775-786.

[5] ?ermák J, Jánský J. On the asymptotics of the trapezoidal rule for the pantograph equation[J]. Math. Comput., 2009, 78(268):2107-2126.

[6] ?ermák J. The stability and asymptotic properties of the θ-methods for the pantograph equation[J]. IMA J. Numer. Anal., 2011, 31:1533-1551.

[7] Engelborghs K, Roose D. On stability of LMS methods and characteristic roots of delay differential equations[J]. SIAM J. Numer. Anal., 2002, 40(2):629-650.

[8] Huang C. Stablity analysis of general linear methods for nonautonomous pantograph equation[J]. IMA J. Numer. Anal., 2009, 29:444-465.

[9] Iserles A. On the generalized pantograph functional-differential equation[J]. Eur. J. Appl. Math., 1993, 4:1-38.

[10] Iserles A, Liu Y. On neutral functional-differential equations with proportional delays[J]. J. Math. Anal. Appl., 1997, 207:73-95.

[11] Lehniger H, Liu Y. The functional-differential equation y'(t)=Ay(t) + By(λt) + Cy'(qt) + f(t)[J]. Eur. J. Appl. Math., 1998, 9:81-91.

[12] Levin C, Pecaric J, Sarapa N. A note on Chung's strong law of large numbers[J]. J. Math. Anal. Appl. 1998, 217(1):328-334.

[13] Li Y. Positive periodic solution of neutral Lotka-Volterra system with state dependent delays[J]. J. Math. Anal. Appl., 2007, 330:1347-1362.

[14] Liu Y. Asymptotic behavior of functional-differential equations with proportional time delays[J]. Eur. J. Appl. Maths., 1996, 7:11-30.

[15] Liu Y. Regular solutions of the Shabat equation[J]. J. Differ. Equations, 1999, 154:1-41.

[16] Liu Z, Chen L. Periodic solution of neutral Lotka-Volterra system with periodic delays[J]. J. Math. Anal. Appl., 2006, 324:435-451.

[17] Lu S, Ge W. Existence of positive periodic solution for neutral population model with taultiple delay[J]. Appl. Math. Comp., 2004, 153:885-905.

[18] Ockendon J R, Tayler A B. The dynamics of a current collection system for an electric locomotive[J]. Proc. R. Soc. A. 1971, 322:447-468.

[19] Wang W, Li S. Stability analysis of θ-methods for nonlinear neutral delay differential equations[J]. SIAM J. Sci. Comput., 2007, 193:285-301.

[20] Wang W, Li S, Su K. Nonlinear stability of Runge-Kutta methods for neutral delay differential equations[J]. J. Comput. Appl. Math., 2008, 214:175-185.

[21] Wang W, Zhang Y, Li S. Nonlinear stablity of one-leg methods for delay differential equations of neutral type[J]. Appl. Numer. Math., 2008, 58:122-130.

[22] Wang W, Li S, Su K. Nonlinear stablity of general linear methods for neutral delay differential equations[J]. J. Comput. Appl. Math., 2009, 224:592-601.

[23] Wang W, Zhang Y, Li S. Stability of continuous Runge-Kutta methods for nonlinear neutral delay-differential equations[J]. Appl. Math. Model., 2009, 33:3319-3329.

[24] Zhang G, Xiao A, Wang W. The asymptotic behaviour of the θ-methods with constant stepsize for the generalized pantograph equation[J]. Int. J. Comput. Math., 2016, 93(9):1484-1504.

[25] Zhao J, Cao W, Liu M. Asymptotic stability of Runge-Kutta methods for the pantograph equations[J]. J. Comput. Math., 2004, 22(4):523-534.

[1]王晚生,李寿佛,苏凯,. 求解非线性中立型延迟微分方程一类线性多步方法的收敛性[J]. 计算数学, 2008, 30(2): 157-166.
[2]余越昕,李寿佛,. 非线性中立型延迟微分方程单支方法的数值稳定性[J]. 计算数学, 2006, 28(4): 357-364.
[3]王晚生,李寿佛. 非线性中立型延迟微分方程稳定性分析[J]. 计算数学, 2004, 26(3): 303-314.

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=74
相关话题/数学 计算 推荐 比例 阅读