| 非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性 |
| |
| 引用本文： | 王琳,许珊珊,王文强.非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性[J].计算数学,2023,45(1):57-73. |
| |
| 作者姓名： | 王琳 许珊珊 王文强 |
| |
| 作者单位： | 湘潭大学科学工程计算与数值仿真湖南省重点实验室, 湘潭 411105 |
| |
| 基金项目： | 国家自然科学基金(12071403)和湖南省教育厅重点项目(18A049)资助. |
| |
| 摘 要： | 本文研究了一类新的模型问题:非线性随机分数阶延迟积分微分方程.当方程中的漂移项和扩散项满足全局Lipschitz条件和线性增长条件时,基于压缩映射原理给出了该方程解存在唯一的充分条件.由于理论求解的困难,构造了一种数值方法(Euler-Maruyama方法),并证得强收敛阶为α-1/2,α∈(1/2,1].最后通过数值试验,验证了这一理论结果.
|
| 关 键 词： | 随机分数阶延迟积分微分方程 Eluer-Maruyama方法 强收敛性 解的存在唯一性 Caputo分数微分算子 |
| 收稿时间： | 2021-07-01 |
STRONG CONVERGENCE OF THE ELUER-MARUYAMA METHOD FOR STOCHASTIC FRACTIONAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS |
| |
| Wang Lin,Xu Shanshan,Wang Wenqiang.STRONG CONVERGENCE OF THE ELUER-MARUYAMA METHOD FOR STOCHASTIC FRACTIONAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J].Mathematica Numerica Sinica,2023,45(1):57-73. |
| |
| Authors: | Wang Lin Xu Shanshan Wang Wenqiang |
| |
| Affiliation: | Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China |
| |
| Abstract: | This paper studies a new type of model problem: nonlinear stochastic fractional delay integro-differential equations. Under the assumptions that the drift and diffusion terms in the equation satisfy the global Lipschitz condition and linear growth condition, the existence and uniqueness of the solution is proved by using contraction mapping principle. Due to the difficulty of theoretical solution, a numerical method (Euler-Maruyama method) is constructed and the order of strong convergence is proved to be α-1/2, α∈(1/2, 1].Finally, the theoretical results are verified by numerical experiments. |
| |
| Keywords: | Stochastic fractional delay integro-differential equation Eluer-Maruyama method Strong convergence Existence and uniqueness of solution Caputo fractional differential operator |
|
| 点击此处可从《计算数学》浏览原始摘要信息 |
|
点击此处可从《计算数学》下载全文 |
