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一类非线性延迟微分方程数值解的振动性分析

宋福义, 高建芳   

  1. 哈尔滨师范大学数学科学学院, 哈尔滨 150025
  • 收稿日期:2014-11-06 出版日期:2015-11-15 发布日期:2015-11-19
  • 通讯作者: 高建芳,E-mail: 09151108@163.com.
  • 基金资助:

    黑龙江省教育厅科学技术研究项目(12541244).

宋福义, 高建芳. 一类非线性延迟微分方程数值解的振动性分析[J]. 计算数学, 2015, 37(4): 425-438.

Song Fuyi, Gao Jianfang. Oscillation analysis of numerical solutions for a kind of nonlinear delay differential equation[J]. Mathematica Numerica Sinica, 2015, 37(4): 425-438.

Oscillation analysis of numerical solutions for a kind of nonlinear delay differential equation

Song Fuyi, Gao Jianfang   

  1. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
  • Received:2014-11-06 Online:2015-11-15 Published:2015-11-19
本文考虑一类非线性延迟微分方程-带有单调造血率的造血模型数值解的振动性. 通过研究特征方程根的情况得到数值解振动的条件并且讨论了非振动的数值解的一些性质. 为了更有力的说明我们的结果, 最后给出了相应的算例.
This paper is concerned with oscillations of numerical solutions for nonlinear delay differential equation of hematopoiesis with a monotone production rate. By investigating the roots of characteristic equation, some conditions under which the numerical solution is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments.

MR(2010)主题分类: 

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[1] Jhon R Graef, Saroj Panigrahi and P Rami Reddy. On Oscillatroy and Asymptotic Behaviour of Fourth Order Nonlinear Neutral Delay Dynamic Equations with Positive and Negative Coefficients[J]. Math. Slovaca, 2014, 64(2):347-366.

[2] Chen F. Oscillatory and Asymptotic Behaviour of Odd Order Delay Differential Equations with Impulses[J]. Journal of Mathematical Sciences, 2013, 15(2):258-273.

[3] Zhang C, Li T and Saker S H. Oscillation of Fourth Order Delay Differential Equations[J]. Journal of Mathematical Sciences, 2014, 201(3):322-335.

[4] Fatma Karakoc, Huseyin Bereketoglu and Gizem Seyhan. Oscillatory and Periodic Solutions of Impulsive Differential Equations with Piecewise Constant Argument[J]. Acta. Appl. Math., 2010, 110:499-510.

[5] Seshadev padhi and Smita Pati. Theory of Third-Order Differential Equations[M]. India:Springer, 2014, 335-453.

[6] R.Koplatadze and S.Pinelas. On Oscillation of Solutions of Second-Order Nonlinear Difference Equations[J]. Journal of Mathematical Sciences, 2013, 189(5):0784-0794.

[7] Zheng Yu, Zhu E W and Zeng J S. On the Oscillation of Solutions for a Class of Second-Order Nonlinear Stochastic Difference Equations[J]. Adva. Diff. Equa., 2014, (91).

[8] Chatzarakis G E, Pinelas S and Stavroulakis I P. Oscillations of Difference Equations with Several Deviated Arguments[J]. Aequat. Math., 2014, 88:105-123.

[9] Kubiaczyk I, Saker S H and Sikorska-nowak A. Oscillation Criteria for Nonlinear Neutral Functional Dynamic Equations on Times Scales[J]. Math. Slovaca., 2013, 63(2):263-290.

[10] Leonid Berezansky, Elena Braveman and Lev Idels. Mackey-Glass Model of Hematopoiesis with Non-Monotone Feedback:Stability,Oscillation and Control[J]. Appl. Math. Comput., 2013, 219:6268-6283.

[11] Sobolev G A. On Some Properties in the Emergence and Evolution of the Oscillations of the Earth after Earthquakes[J]. Physics of the Solid Earth, 2013, 49(5):610-625.

[12] Liu M Z, Gao J F Yang Z W. Oscillation Analysis of Numerical Solution in the θ-methods for Equation x'(t)+ax(t)+a1x([t-1] )=0[J]. Appl. Math. Comput., 2007, 186:566-578.

[13] Liu M Z, Gao J F, Yang ZW. Preservation of Oscillation of the Runge-Kutta Method for Equation x'(t)+ax(t)+a1x([t-1] )=0[J]. Comput. Math. Appl., 2009, 58:1113-1125.

[14] Song M H, Liu M Z. Numerical Stability and Oscillation of the Runge-KuttaMethods for Equation x'(t)=ax(t)+a0x(M[t+N/M])[J]. Adva. Diff. Equa., 2012, 146.

[15] Gao J F, Song M H and Liu M Z. Oscillation Analysis of Numerical Solutions for Nonlinear Delay Differential Equations of Population Dynamics[J]. Math. Model. Anal., 2011, 16(3):365-375.

[16] Wang Q, Wen J C, Qiu S S and Guo C. Numerical Oscillations for First Order Nonlinear Delay Differential Equations in a Hematopoiesis Model[J]. Adva. Diff. Equa., 2013, 163.

[17] Glass L, Mackey M. Mackey-Glass Equation. Scholarpedia, 2010, 5(3):6908.

[18] Mackey M, Glass L. Oscillation and Chaos in Physiological Control Systems. Science, 1977, 197:287-289.

[19] MackeyM, U. an der Heiden, Dynamic Diseases and Bifurcations in Physiological Control Systems. Funk. Biol. Med., 1982, 1:156-164.

[20] Mackey M. Mathematical Models of Hematopoietic Cell Replication and Control, in:H.G. Othmer, F.R. Adler, M.A. Lewis, J.C. Dallon (Eds.), The Art of Mathematical Modelling:Case Studies in Ecology, Physiology and Biofluids. Prentice Hall, 1997, 149-178.

[21] Györi I, Ladas G. Oscillation Theory of Delay Equations with Applications[M]. Oxford:Clarendon Press, 1991, 32-197.

[22] Hale J K. Theory of Functional Differential Equations[M]. New York:Applied Mathematical Sciences, 1977, 11-190.

[23] Wanner G, Hairer E, Norsett S P. Solving Ordinary Differential Equations I:Nonstiff Problems[M]. Berli Heidelberg:Springer-Verlag, 1993, 129-353.

[24] Song M H, Yang Z W and Liu M Z. Stability of θ-methods for Advanced Differential Equations with Piecewise Continuous Arguments[J]. Comput. Math. Appl., 2005, 49:1295-1301.
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