非线性随机比例方程数值解的收敛率(英文)  

Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations

作　　者：胡军浩[1] 胡艳寒[1] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2013年第1期106-111,共6页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(60904005);湖北省自然科学基金资助项目(2009CDB026)

摘　　要：主要研究了非线性随机比例方程数值解的收敛率.在比利普希茨条件和线性增长条件更弱的条件下,证明了非线性随机比例方程解的存在性和惟一性,并且给出了其对应的Euler-Maruyama数值解的收敛率为12.特别的,在这些条件下,随机比例方程相应的系数可以是非线性的.In this paper,the convergence rate of numerical solutions for nonlinear stochastic pantograph equations is considered.The existence and uniqueness of the solutions for nonlinear stochastic pantograph equations under conditions which is weaker than Lipschitz condition and linear growth condition is obtained.In particular,under the conditions which permit that the corresponding coefficients can be highly nonlinear,it is proved that the convergence order of Euler-Maruyama schemes is 1/2.

关 键 词：随机比例方程 欧拉方法 收敛率 

分 类 号：O242.28[理学—计算数学]