与年龄相关的模糊随机种群系统的半隐式Euler法的收敛性
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摘要
介绍了一类与年龄相关的模糊随机种群系统的半隐式Euler法.系统同时受到两种不确定性因素的影响:即,随机和模糊.在有界的条件(弱于线性增长条件)和Lipschitz条件下,讨论了与年龄相关的模糊随机种群系统在半隐式Euler法下的收敛性.方法具有克服线性计算不稳定的优点.最后通过例子对算法进行了验证.
In this paper,we introduce a class of semi-implicit methods for stochastic fuzzy age-dependent population equations,where the phenomena is subjected to two sorts of uncertainty:stochastic and fuzziness,simultaneously.Under a boundedness condition,which is weaker than linear growth condition,and the Lipschitz condition we obtain the convergence of semi-implicit Euler methods to stochastic fuzzy age-dependent population equations.This method has the advantage of overcoming nonlinear computational instability.In the last section,a numerical example is given.
In this paper,we introduce a class of semi-implicit methods for stochastic fuzzy age-dependent population equations,where the phenomena is subjected to two sorts of uncertainty:stochastic and fuzziness,simultaneously.Under a boundedness condition,which is weaker than linear growth condition,and the Lipschitz condition we obtain the convergence of semi-implicit Euler methods to stochastic fuzzy age-dependent population equations.This method has the advantage of overcoming nonlinear computational instability.In the last section,a numerical example is given.
引文
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[4]Li R,Pang W,Leung P.Convergence of numerical solutions to stochastic age-structured population equations with diffusions and Markovian switching[J].Appl Math Comput,2010,216:744-752.
[5]申芳芳,张启敏,杨洪福,李西宁.与年龄相关的模糊随机种群扩散系统的指数稳定性[J].数学的实践与认识,2014,7(44):187-195.
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[7]Pang W,Li R,Liu M.Convergence of the semi-implicit Euler method for stochastic age-dependent population equations[J].Appl Math Comput,2008,195:466-474.
[8]Wang L,Wang X.Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps[J].Appl Math Model,2010,34:2034-2043.
[9)苏方伟,胡良剑.模糊随机微分方程解的存在唯一性[J].模糊系统与数学,2009,23(4):66-73.
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[2]li R,Meng H,Chang Q.Convergence of numerical solutions to stochastic age-dependent population equations[J].J Comput Appl Math,2006,193:109-120.
[3]Zhang Q,Wei D.Necessary and suffcient conditions for near-optimal harvesting control problem of stochastic age-dependent system[J].Appl Math Comput,2013,221:394-402.
[4]Li R,Pang W,Leung P.Convergence of numerical solutions to stochastic age-structured population equations with diffusions and Markovian switching[J].Appl Math Comput,2010,216:744-752.
[5]申芳芳,张启敏,杨洪福,李西宁.与年龄相关的模糊随机种群扩散系统的指数稳定性[J].数学的实践与认识,2014,7(44):187-195.
[6]Chen N,Xu Z,Xia M.Correlation coeffcients of hesitant fuzzy sets and their applications to clustering analysis[J].Appl Math Model,2013,37:2197-2211.
[7]Pang W,Li R,Liu M.Convergence of the semi-implicit Euler method for stochastic age-dependent population equations[J].Appl Math Comput,2008,195:466-474.
[8]Wang L,Wang X.Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps[J].Appl Math Model,2010,34:2034-2043.
[9)苏方伟,胡良剑.模糊随机微分方程解的存在唯一性[J].模糊系统与数学,2009,23(4):66-73.
[10]MaUnowski M T.Some properties of strong solutions to stochastic fuzzy differential equations[J].Information Sciences,2013,252:62-80.
[11]Malinowski M T.Strong solutions to stochastic fuzzy differential equations of Ito type[J].Math Comput Modell,2012,55:918-928.