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代新杰

2023-09-14    点击:[]


教师姓名:代新杰

   称:副教授

   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:

2015.092021.06 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

2011.092015.06 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 永利二维码推广副教授

2021.072023.06 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) 1933

[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) 1838


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:2022M7133132022–2023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CX201904202019–2021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:120714032021–2024参加

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:116713432017–2020 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 AlgorithmsFractional Calculus and Applied AnalysisJournal of Computational and Applied Mathematics等多个SCI期刊审稿。


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