Mean-square dissipativity of two numerical methods for stochastic age-dependent population equations with jumps
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摘要: 讨论了一类与年龄相关的随机种群模型数值解的均方散逸性: 基于步长~h~受限制和无限制的两种条件, 利用倒向欧拉法和补偿的倒向欧拉法分析了该随机种群模型数值解的均方散逸性并加以证明, 最后得出补偿的倒向欧拉法更适合解决与年龄相关的随机种群模型数值解的均方散逸性问题.
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关键词:
- 均方散逸性
Abstract: 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.-
Keywords:
- mean-square dissipativity
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[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.
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