• Overview of Chinese core journals
  • Chinese Science Citation Database(CSCD)
  • Chinese Scientific and Technological Paper and Citation Database (CSTPCD)
  • China National Knowledge Infrastructure(CNKI)
  • Chinese Science Abstracts Database(CSAD)
  • JST China
  • SCOPUS
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.
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.

Mean-square dissipativity of two numerical methods for stochastic age-dependent population equations with jumps

More Information
  • Received Date: January 09, 2016
  • Revised Date: June 23, 2016
  • The mean-square dissipativity of the numerical solution for a class of stochastic age-dependent population equations with jumps is discussed. Based on the step length under the condition of limited and unlimited, it is essential for studying the mean-square dissipativity to use backward Euler method and compensated backward Euler method for stochastic age-dependent population equations with jumps. The results show that the compensated backward Euler method is more suitable for solving the mean-square dissipativity about stochastic age-dependent population equations with jumps.
  • [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.

Catalog

    Article views (892) PDF downloads (184) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return