Citation: | Mean-square dissipativity of two numerical methods for stochastic age-dependent population equations with jumps[J]. Journal of South China Normal University (Natural Science Edition), 2017, 49(4): 106-110. |
[1] A. M. Stuart, A. R. Humphries, Dynamical Systems and Numerical Analysis[M]. Cambridge University Press, Cambridge, 1996.
[2] S. Gan, Exact and discretized dissipativity of the pantograph equation[J]. J. Comput. Math, 2007, 25: 81–88. [3] S. Gan, Dissipativity of θ-methods for nonlinear delay differential equations of neutraltype[J]. Appl. Numer. Math, 2009, 59: 1354–1365. [4] X. Liu, L. Wen, Dissipativity of one-leg methods for neutral delay integro-differential equations[J]. J. Comput. Appl. Math, 2010, 235: 165–173. [5] L. Wang, X. Ding, Dissipativity of θ-methods for a class of nonlinear neutral delay integrodifferential equations[J]. Int. J. Comput. Math, 2012, 89 (15): 2029–2046. [6] Qimin Zhang,Wenan Liu, Zankan Nie. Existence, uniqueness and expoenential stability for stochastic age-dependent population[J]. Applied Mathematics and Computation, 2004, 154: 183–201. [7] Jianguo Tan, A Rathinasamy, Yongzhen Pei. Convergence of the split-step θ-method for stochastic age-dependent population equations with Possion jumps[J]. Applied Mathematics and Computation, 2015, 254: 305–317. [8] A. Rathinasamy, Split-step θ-methods for stochastic age-dependent population equations with Markovian switching[J]. Nonlinear Analysis: Real Word Applications, 2012, 13: 1334–1345. [9] 金小薇, 张启敏. 带Poisson 跳的模糊随机种群扩散方程解的存在性与唯一性[J]. 华南师范大学学报(自然科学版), 2014, 46(4): 16–21. [10] 张彦山, 张启敏. 一类与年龄相关的种群系统的数值解[J]. 应用数学学报, 2009, 22(2): 303–309. [11] Weijun Ma, Qimin Zhang, Chongzhao Han. Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion[J]. Commun Nonlinear Sci Numer Simulat, 2012, 17: 1884–1893. [12] Qiang Ma, Deqiong Ding, Xiaohua Ding. Mean-square dissipativity of several numerical methods for stochastic differential equations with jumps[J]. Applied Numerical Mathematics, 2014, 82: 44–50.
[1] A. M. Stuart, A. R. Humphries, Dynamical Systems and Numerical Analysis[M]. Cambridge University Press, Cambridge, 1996.
[2] S. Gan, Exact and discretized dissipativity of the pantograph equation[J]. J. Comput. Math, 2007, 25: 81–88. [3] S. Gan, Dissipativity of θ-methods for nonlinear delay differential equations of neutraltype[J]. Appl. Numer. Math, 2009, 59: 1354–1365. [4] X. Liu, L. Wen, Dissipativity of one-leg methods for neutral delay integro-differential equations[J]. J. Comput. Appl. Math, 2010, 235: 165–173. [5] L. Wang, X. Ding, Dissipativity of θ-methods for a class of nonlinear neutral delay integrodifferential equations[J]. Int. J. Comput. Math, 2012, 89 (15): 2029–2046. [6] Qimin Zhang,Wenan Liu, Zankan Nie. Existence, uniqueness and expoenential stability for stochastic age-dependent population[J]. Applied Mathematics and Computation, 2004, 154: 183–201. [7] Jianguo Tan, A Rathinasamy, Yongzhen Pei. Convergence of the split-step θ-method for stochastic age-dependent population equations with Possion jumps[J]. Applied Mathematics and Computation, 2015, 254: 305–317. [8] A. Rathinasamy, Split-step θ-methods for stochastic age-dependent population equations with Markovian switching[J]. Nonlinear Analysis: Real Word Applications, 2012, 13: 1334–1345. [9] 金小薇, 张启敏. 带Poisson 跳的模糊随机种群扩散方程解的存在性与唯一性[J]. 华南师范大学学报(自然科学版), 2014, 46(4): 16–21. [10] 张彦山, 张启敏. 一类与年龄相关的种群系统的数值解[J]. 应用数学学报, 2009, 22(2): 303–309. [11] Weijun Ma, Qimin Zhang, Chongzhao Han. Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion[J]. Commun Nonlinear Sci Numer Simulat, 2012, 17: 1884–1893. [12] Qiang Ma, Deqiong Ding, Xiaohua Ding. Mean-square dissipativity of several numerical methods for stochastic differential equations with jumps[J]. Applied Numerical Mathematics, 2014, 82: 44–50. |