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随机比例方程带线性插值的半隐式Euler方法的均方收敛性

张浩敏1, 甘四清2, 胡琳2,3   

  1. 1. 桂林理工大学理学院, 广西桂林 541004;
    2. 中南大学数学科学与计算技术学院, 长沙 410075;
    3. 东北林业大学数学系, 哈尔滨 150041
  • 收稿日期:2008-06-11 出版日期:2009-12-15 发布日期:2009-12-30
  • 基金资助:

    国家自然科学基金(10871207,10571147)资助项目

张浩敏, 甘四清, 胡琳. 随机比例方程带线性插值的半隐式Euler方法的均方收敛性[J]. 计算数学, 2009, 31(4): 379-392.

Zhang Haomin, Gan Siqing, Hu Lin. MEAN SQUARE CONVERGENCE OF SEMI-IMPLICIT EULER METHODS WITH LINEAR INTERPOLATION FOR STOCHASTIC PANTOGRAPH EQUATIONS[J]. Mathematica Numerica Sinica, 2009, 31(4): 379-392.

MEAN SQUARE CONVERGENCE OF SEMI-IMPLICIT EULER METHODS WITH LINEAR INTERPOLATION FOR STOCHASTIC PANTOGRAPH EQUATIONS

Zhang Haomin1, Gan Siqing2, Hu Lin2,3   

  1. 1. School of Science, Guilin University of Technology, Guilin 541004, Guangxi, China;
    2. School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China;
    3. Department of Mathematics, Northeast Forestry University, Harbin 150041, China
  • Received:2008-06-11 Online:2009-12-15 Published:2009-12-30
本文研究非线性随机比例方程带线性插值的半隐式Euler方法的均方收敛性,证明了这类方法是1/2阶均方收敛的.数值试验验证了所获理论结果的正确性.

 

In this paper, the mean square convergence of semi-implicit Euler methods with linear interpolation for nonlinear stochastic pantograph equations is discussed and it is shown that these methods are mean square convergent with order 1/2. A nonlinear numerical example is presented to illustrate the theoretical result.

 

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