教师姓名：代新杰

职    称：副教授

系    所：数学系

主要研究领域：随机积分方程数值方法

电子邮件：dxj@ynu.edu.cn

个人主页：https://orcid.org/0000-0002-9038-4903

教育背景：

2015.09至2021.06 湘潭大学数学与计算科学学院，数学专业（硕博连读），理学博士

2011.09至2015.06 中南林业科技大学理学院，信息与计算科学专业，理学学士

工作经历：

2023.09至今 云南大学数学与统计学院，副教授

2021.07至2023.06 中国科学院数学与系统科学研究院，博士后

代表性学术论著：（注：带“*”为通讯作者）

[1] X. Dai, J. Hong, D. Sheng, Error analysis of numerical methods on graded meshes for stochastic Volterra equations, Preprint (2023) arXiv: 2308.16696

[2] X. Dai, J. Hong, D. Sheng, T. Zhou, Strong error analysis of Euler methods for overdamped generalized Langevin equations with fractional noise: nonlinear case, ESAIM Math. Model. Numer. Anal. 57 (2023) 1981–2006

[3] X. Dai, J. Hong, D. Sheng, Mittag–Leffler Euler integrator and large deviations for stochastic space-time fractional diffusion equations, Potential Anal. (2023) DOI: 10.1007/s11118-023-10090-9

[4] X. Dai, A. Xiao, Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method, Adv. Comput. Math. 46 (2020) 29

[5] X. Dai, A. Xiao, A note on Euler method for the overdamped generalized Langevin equation with fractional noise, Appl. Math. Lett. 111 (2021) 106669

[6] X. Dai, A. Xiao, W. Bu, Stochastic fractional integro-differential equations with weakly singular kernels: well-posedness and Euler–Maruyama approximation, Discrete Contin. Dyn. Syst. Ser. B 27 (2022) 4231–4253

[7] X. Dai, A. Xiao, Numerical solutions of nonautonomous stochastic delay differential equations by discontinuous Galerkin methods, J. Comput. Math. 37 (2019) 419–436

[8] X. Dai, W. Bu, A. Xiao, Well-posedness and EM approximations for non-Lipschitz stochastic fractional integro-differential equations, J. Comput. Appl. Math. 356 (2019) 377–390

[9] C. Wang, M. Chen, W. Deng, W. Bu, X. Dai^*, A sharp error estimate of Euler–Maruyama method for stochastic Volterra integral equations, Math. Methods Appl. Sci. 45 (2022) 6005–6029

[10] M. Li, X. Dai, C. Huang, Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent, Numer. Algorithms 92 (2023) 2433–2455

[11] M. Wang, X. Dai, Y. Yu, A. Xiao, Fast θ-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis, Comp. Appl. Math. 42 (2023) 108

[12] H. Tang, X. Dai, M. Wang, A. Xiao, Singular stochastic Volterra integral equations with Mittag–Leffler kernels: well-posedness and strong convergence of θ-Maruyama method, Int. J. Comput. Math. 100 (2023) 1321–1339

[13] M. Wang, X. Dai, A. Xiao, Optimal convergence rate of θ-Maruyama method for stochastic Volterra integro-differential equations with Riemann–Liouville fractional Brownian motion, Adv. Appl. Math. Mech. 14 (2022) 202–217

[14] G. Zhang, X. Dai, Superconvergence of discontinuous Galerkin method for neutral delay differential equations, Int. J. Comput. Math. 98 (2021) 1648–1662

[15] G. Zhang, G. He, X. Dai, Stability analysis of discontinuous Galerkin method for stiff Volterra functional differential equations, J. Math. Anal. Appl. 475 (2019) 1293–1303

[16] Y. Yu, X. Dai^*, A. Xiao, Convergence and stability of the canonical EM splitting method for nonautonomous stiff stochastic differential equations (Chinese), Math. Numer. Sin. 44 (2022) 19–33

[17] J. Peng, X. Dai^*, A. Xiao, W. Bu, Strong convergence of the split-step θ method for neutral stochastic delay differential equations (Chinese), Math. Numer. Sin. 42 (2020) 18–38

代表性教学科研项目：

1. 博士后科学基金面上项目：广义Langevin方程的数值方法，批准号：2022M713313，2022–2023（主持，已结题）

2. 湖南省研究生科研创新重点项目：随机分数阶积分微分方程的理论分析与数值方法，批准号：CX20190420，2019–2021（主持，已结题）

3. 国家自然科学基金面上项目：几类记忆型微分方程初值问题的数值方法，批准号：12071403，2021–2024（参加）

4. 国家自然科学基金面上项目：几类非局部微分方程的高效保结构算法，批准号：11671343，2017–2020 （参加，已结题）

获奖情况：

1. 博士研究生国家奖学金

2. 湖南省计算数学应用软件学会青年优秀论文奖

3. 湖南省研究生创新论坛优秀论文一等奖

主要学术任职：

担任美国《数学评论》评论员，以及为Numerical Algorithms、Fractional Calculus and Applied Analysis、Journal of Computational and Applied Mathematics等多个SCI期刊审稿。