宋福义, 高建芳
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.
Song Fuyi, Gao Jianfang
MR(2010)主题分类:
分享此文:
| [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. |
| [1] | 包学忠, 胡琳. 随机变延迟微分方程平衡方法的均方收敛性与稳定性[J]. 计算数学, 2021, 43(3): 301-321. |
| [2] | 张根根, 肖爱国, 王晚生. 中立型比例延迟微分系统线性θ-方法的渐近估计[J]. 计算数学, 2020, 42(4): 419-434. |
| [3] | 彭捷, 代新杰, 肖爱国, 卜玮平. 中立型随机延迟微分方程分裂步θ方法的强收敛性[J]. 计算数学, 2020, 42(1): 18-38. |
| [4] | 杨水平. 一类分数阶多项延迟微分方程的Jacobi谱配置方法[J]. 计算数学, 2017, 39(1): 98-114. |
| [5] | 许秀秀, 黄秋梅. 拟等级网格下非线性延迟微分方程间断有限元法[J]. 计算数学, 2016, 38(3): 281-288. |
| [6] | 赵卫东. 正倒向随机微分方程组的数值解法[J]. 计算数学, 2015, 37(4): 337-373. |
| [7] | 陈一鸣, 孙艳楠, 刘立卿, 柯小红. 基于拟Legendre多项式求解一类分数阶微分方程[J]. 计算数学, 2015, 37(1): 21-33. |
| [8] | 王琦, 汪小明. 单物种人口模型指数隐式Euler方法的振动性[J]. 计算数学, 2015, 37(1): 57-66. |
| [9] | 闵文超, 黎稳, 柯日焕. 求解Hubbard线性系统的快速稳定算法[J]. 计算数学, 2014, 36(1): 1-15. |
| [10] | 王文强, 李东方. 线性变系数中立型变延迟微分方程谱方法的收敛性[J]. 计算数学, 2012, 34(1): 68-80. |
| [11] | 高建芳, 张艳英, 唐黎明. 种群动力系统的数值解的振动性分析[J]. 计算数学, 2011, 33(4): 357-366. |
| [12] | 范振成, 宋明辉. 非全局Lipschitz条件下随机延迟微分方程Euler方法的收敛性[J]. 计算数学, 2011, 33(4): 337-344. |
| [13] | 张春赛, 胡良剑. 时滞均值回复θ过程及其数值解的收敛性[J]. 计算数学, 2011, 33(2): 185-198. |
| [14] | 谭英贤, 甘四清, 王小捷. 随机延迟微分方程平衡方法的均方收敛性与稳定性[J]. 计算数学, 2011, 33(1): 25-36. |
| [15] | 王文强, 陈艳萍. 非线性随机延迟微分方程Heun方法的数值稳定性[J]. 计算数学, 2011, 33(1): 69-76. |
| 阅读次数 | ||||||
|
全文 |
|
|||||
|
摘要 |
|
|||||
