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随机分数阶微分方程初值问题基于模拟方程法的数值求解

孙春艳 徐伟

孙春艳, 徐伟. 随机分数阶微分方程初值问题基于模拟方程法的数值求解[J]. 应用数学和力学, 2014, 35(10): 1092-1099. doi: 10.3879/j.issn.1000-0887.2014.10.003
引用本文: 孙春艳, 徐伟. 随机分数阶微分方程初值问题基于模拟方程法的数值求解[J]. 应用数学和力学, 2014, 35(10): 1092-1099. doi: 10.3879/j.issn.1000-0887.2014.10.003
SUN Chun-yan, XU Wei. An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1092-1099. doi: 10.3879/j.issn.1000-0887.2014.10.003
Citation: SUN Chun-yan, XU Wei. An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1092-1099. doi: 10.3879/j.issn.1000-0887.2014.10.003

随机分数阶微分方程初值问题基于模拟方程法的数值求解

doi: 10.3879/j.issn.1000-0887.2014.10.003
基金项目: 国家自然科学基金(11772233)
详细信息
    作者简介:

    孙春艳(1984—),女,山东威海人,博士生(通讯作者. E-mail: sunchunyan@mail.nwpu.edu.cn).

  • 中图分类号: O322;O324

An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations

Funds: The National Natural Science Foundation of China(11772233)
  • 摘要: 基于模拟方程法,提出了一种求解随机分数阶微分方程初值问题的数值方法.考虑含两个分数阶导数项的微分方程,引入两个线性的、非耦合的随机模拟方程,利用它们解构原方程,借助Laplace变换及逆变换,得到方程解的积分表达式,同时建立起两个模拟方程之间的联系,结合初始状态,得到求解随机微分方程初值问题的数值迭代算法.作为特例,对于含两个分数阶导数项线性常微分方程的初值问题,给出了基于模拟方程法的数值解法的显式结果.该方法是稳定的,它的误差仅存在于积分近似时的截断误差和计算软件的舍入误差.应用实例说明了数值方法在确定和随机情形的有效性和准确性.
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出版历程
  • 收稿日期:  2014-05-19
  • 修回日期:  2014-09-08
  • 刊出日期:  2014-10-15

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