头像
曹婉容
教授
威斯尼斯人60555入口官网
计算数学系
电话：
邮箱：
wrcao@seu.edu.cn
地址：
湖区图书馆北五楼547-2
邮编：
211189
  • 基本信息
  • 研究成果
  • 项目与荣誉
  • 社会兼职
  • 曹婉容，教授，博士生导师. 2004年在哈尔滨工业大学获得理学博士学位后，加入威斯尼斯人60555入口官网数学系。2008年晋升为副教授、硕士生导师，2017年晋升为教授，博士生导师。2010年9月至2011年8月获国家留学基金委资助访问布朗大学应用数学系，并分别于2012年5月到8月、2013年6月到8月、2014年6月到8月、2015年6月到7月作为访问副教授在布朗大学应用数学系进行学术研究与交流合作。累积发表学术论文 40 余篇，其中被SCI收录30 余篇，他引 900 余次. 主讲《随机模型及计算》、《数值分析》，以及研究生《随机微分方程数值解》、《数值分析》等课程，主编教学参考书《数值分析全真试题解析》.
    本人的研究方向为微分方程数值解. 目前的研究兴趣为随机常微分方程、随机偏微分方程、分数阶微分方程及延迟微分方程的高效数值方法，包括数值方法的建立、收敛性与稳定性分析、刚性及非线性问题的数值算法，以及生物、控制、金融等领域中相关应用问题的数值模拟与大规模计算等. 目前主持在研国家自然科学基金项目一项。
    欢迎对上述研究方向感兴趣的同学报考我的硕士研究生、博士研究生，也欢迎已取得博士学位的青年学者加入我们的课题组做博士后。

  • 已发表论文：

    47. Yibo Wang, Wanrong Cao*, Exponential integrator for stochastic strongly damped wave equation based on the Wong-Zakai approximation, Journal of Computational and Applied Mathematics, 437 (2024), 115459.

    46. Nan Deng, Wanrong Cao*, On strong convergence of two numerical methods for singular initial value problems with multiplicative white noise, Journal of Computational and Applied Mathematics, 445 (2024), 115801.

    45. Chengqiang Xu, Yibo Wang, Wanrong Cao*, On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations, Numerical Methods for Partial Differential Equations, DOI: 10.1002/num.23094, 2024.

    44. Shengyue Li, Wanrong Cao*, On spectral Petrov–Galerkin method for solving optimal control problem governed by fracional diffusion equations with fractional noise, Journal of Scientific Computing, 94 (2023), 62.

    43. Yibo Wang, Wanrong Cao*, Strong 1.5 order scheme for fractional Langevin equation based on spectral approximation of white noise, Numerical Algorithm, DOI: 10.1007/s11075-023-01576-z, 2023.

    42. Hong Sun, Wanrong Cao*, Ming Zhang, Energy stability of a temporal variable-step difference scheme for time-fractional nonlinear fourth-order reaction–diffusion equation, International Journal of Computer Mathematics, 100 (5) (2023), 991-1008.

    41. Yan Li, Wanrong Cao*, A positivity preserving Lamperti transformed Euler-Maruyama method for solving the stochastic Lotka-Volterra competition model, Communications in Nonlinear Science and Numerical Simulation, 122 (2023), 107260.

    40. Yufen Liu, Wanrong Cao*, Zhongqiang Zhang, Strong 1.5 order scheme for second-order stochastic differential equations without Levy area, Applied Numerical Mathematics, 184 (2023), 273-284.

    39. Wanrong Cao, Zhaopeng Hao, Zhognqiang Zhang*, Optimal strong convergence of finite element methods for one-dimensional stochastic elliptic equations with fractional noise, Journal of Scientific Computing, 91 (2022), 1.

    38. Nan Deng, Wanrong Cao*, Guofei Pang, On numerical methods to second-order singular initial value problems with additive white noise, Journal of Computational and Applied Mathematics, 416 (2022), 114539.

    37. Shengyue Li, Wanrong Cao*, Zhaopeng Hao, An extrapolated finite difference method for two-dimensional fractional boundary value problems with non-smooth solution, International Journal of Computer Mathematics, 99 (2) (2022), 274-291.

    36. Yufen Liu, Wanrong Cao*, Yulin Li, Split-step balanced theta-method for SDEs with non-globally Lipschitz continuous coefficients, Applied Mathematics and Computation, 413 (2022), 126437.

    35. Shengyue Li, Wanrong Cao*, Yibo Wang, On spectral Petrov-Galerkin method for solving optimal control problem governed by a two-sided fractional diffusion equation, Computers & Mathematics with Applications, 107 (2022), 104-116.

    34. Yibo Wang, Wanrong Cao*, Shengyue Li, A spectral Petrov-Galerkin method for optimal control problem governed by a fractional ordinary differential equation, Applied Numerical Mathematics, 177 (2022), 18-33.

    33. Wanrong Cao*, Jia Liang, Yufen Liu, On strong convergence of explicit numerical methods for stochastic delay differential equations under non-global Lipschitz conditions, Journal of Computational and Applied Mathematics, 382 (2021), 113079.

    32. Zhaopeng Hao, Wanrong Cao*, Shengyue Li, Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity, Numerical Algorithm, 86 (3) (2021), 1071-1087.

    31. Hong Sun, Wanrong Cao*, A fast temporal second-order difference scheme for the time-fractional subdiffusion equation, Numerical Methods for Partial Differential Equations, 37 (3) (2021), 1825-1846.

    30. Jinye Shen, Zhizhong Sun, Wanrong Cao*, A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation, Applied Mathematics and Computation, 361 (2019), 752-765. 

    29. 李学艳，曹婉容*, 分数阶布朗运动驱动的随机延迟微分方程数值解，高等学校计算数学学报，39 (4) (2017), 289-315.  

    28. Zhaopeng Hao, Wanrong Cao*,An improved algorithm based on finite difference schemes for fractional  boundary value problems with nonsmooth solution, Journal of Scientific Computing, 73 (1) (2017), 395-415. 

    27. Zhaopeng Hao, Wanrong Cao*, Guang Lin, A second-order difference scheme for the  time fractional substantial diffusion equation, Journal of Computational and Applied Mathematics, 313 (2017), 54-69.  

    26. Wanrong Cao*, Fanhai Zeng, Zhongqiang zhang, George Em Karniadakis,  Implicit-Explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions, SIAM J. Sci. Comput., 38 (5) (2016), A3070-A3093. 

    25. Zhaopeng Hao, Kai Fan, Wanrong Cao*, Zhizhong Sun, A finite difference scheme for semilinear space-fractional diffusion equations with time delay, Applied Mathematics and Computation, 275 (2016), 238-254. 

    24. Xiuping Li, Wanrong Cao*, On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations, Applied Mathematics and Computation, 261 (2015), 373-381. 

    23. Wanrong Cao*, Zhongqiang zhang, George Em Karniadakis, Time-splitting schemes for fractional differential equations I: Smooth solutions, SIAM J. Sci. Comput.,37 (2015), A1752–A1776.

    22. Wanrong Cao, Zhongqiang zhang, George Em Karniadakis*, Numerical methods for stochastic delay differential equations via the Wong-Zakai approximation, SIAM J. Sci. Comput., 37 (2015), A295-A318.

    21. Zhaopeng Hao, Zhizhong Sun*, Wanrong Cao, A fourth-order approximation of fractional derivatives with its applications, J. Comput. Phys., 281 (2015), 787–805.

    20. Zhaopeng Hao, Zhizhong Sun*, Wanrong Cao, A three-level linearized compact difference scheme for the Ginzburg-Landau equation, Numerical Methods for Partial Differential Equations, 31(3) (2015), 876-899. 

    19. Wanrong Cao*, Peng Hao, Zhongqiang Zhang, Split-step theta-method for stochastic delay differential equations, Appl. Num. Math., 76 (2014), 19-33. 

    18. Mohsen Zayernouri,Wanrong Cao, Zhongqiang zhang, George Em Karniadakis*, Spectral and discontinuous spectral element methods for fractional delay equations, SIAM J. Sci. Comput., 36 (2014), B904-B929.

    17. Wanrong Cao*, Zhongqiang Zhang, On exponential mean-square stability of two-step Maruyama methods for stochastic delay differential equations, J. Comput. Appl. Math., 245 (2013), 182-193. 

    16. Wanrong Cao*, Zhongqiang Zhang, Simulations of two-step Maruyama methods for nonlinear stochastic delay differential equations, Adv. Appl. Math. Mech., 4 (2012), 821-832. 

    15. Wanrong Cao*, Zhizhong Sun.Maximum norm error estimates of Crank- Nicolson scheme for solving a linear moving boundary problem, J. Comput. Appl. Math., 234 (2010), 2578-2586.

    14. Wanrong Cao*, T-stability of the semi-implicit Euler method for delay differential equations with   multiplicative noise，Applied Mathematics and Computation, 216 (2010), 999-1006. 

    13. Ri Du*, Wanrong Cao, Zhizhong Sun, A compact difference scheme for  the fractional diffusion- wave equation, Appl. Math. Model., 34 (2010), 2998-3007.

    12. 郝朝鹏，曹婉容*，求解随机延迟微分方程的分步向前Euler方法，黑龙江大学自然科学学报，30 (2013), 1-7. 

    11. Wanrong Cao. T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise, Appl. Math. Comput., 216 (2010), 999-1006.

    10. Wanrong Cao, Zhizhong Sun. Maximum norm error estimates of Crank-Nicolson scheme for solving a linear   moving boundary problem, J. Comput. Appl. Math., 234 (2010), 2578-2586.

    9. Zhencheng Fan, Mingzhu Liu*, Wanrong Cao. Existence and uniqueness of the solutions and convergence of    semi-implicit Euler methods for stochastic pantograph equations, J. Math. Anal. Appl., 325 (2007),  1142-1159.

    8. Wanrong Cao*. Local convergence of semi-implicit Euler method for a linear stochastic differential delay equation, Journal of natural science of Heilongjiang University, 24 (1) (2007), 97-99,104. (in Chinese)

    7. Wanrong Cao*，Jingjun Zhao, Mingzhu Liu. NGPG-stability of implicit Runge-Kutta method for neutral differential equations with pantograph delay, Journal of system simulation, 19 (2007), 2698-2700, 2705. (in Chinese)

    6. Wanrong Cao，Mingzhu Liu*. Stability of semi-implicit Milstein method for stochastic differential delay equations, Journal of Harbin Institute of Technology, 37 (4) (2005), 446-448. (in Chinese)

    5. Wanrong Cao，Mingzhu Liu*. T-Stability of Euler-Maruyama method for stochastic differential delay equations, Journal of Harbin Institute of Technology, 37 (3) (2005), 303-305, 309. (in Chinese)

    4. Wanrong Cao, Mingzhu Liu*, Zhencheng Fan. MS-stability of the Euler-Maruyama method for stochastic differential delay equations, Appl. Math. Comput., 159 (2004), 127-136.

    3. Mingzhu Liu*, Wanrong Cao, Zhencheng Fan. Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation, J. Comput. Appl. Math., 170 (2004), 255-268.

    2. Jingjiu Zhao*, Wanrong Cao, Mingzhu Liu. Asymptotic stability of Runge-Kutta methods for the pantograph equations, J. Comput. Math., 22 (2004), 523-534.

    1. Wanrong Cao，Jingjun Zhao*, Mingzhu Liu. Stability of new block θ-method for neutral differential   equation with pantograph delay, Journal of system simulation, 15 (6) (2003), 807-809, 822. (in Chinese)



    出版的教材或教辅用书：

    曹婉容，杜睿，吴宏伟，孙志忠，数值分析全真试题解析，威斯尼斯人60555入口官网出版社，2023




  • 科研项目：

    主持国家自然科学基金面上项目，12071073、求解分数布朗运动驱动的几类随机微分方程的数值方法、2021/01-2024/12;

    主持国家自然科学基金面上项目，11671083、求解刚性及非线性随机延迟微分方程的数值方法、2017/01-2020/12;

    参与国家自然科学基金面上项目，11271068、空间分数阶偏微分方程高精度快速算法的研究、2013/01-2016/12 (排名第二);

    主持国家自然科学基金青年基金项目，10901036、求解随机延迟微分方程的多步方法、2010/01-2012/12;

    参与国家自然科学基金面上项目，10771033、椭圆型方程反问题及数值解、2008/01-2010/12 (排名第四).


    教改项目：


    1. 工科研究生《数值分析》教学改革与实践 (No. JGLX18_080), 省级，2018；

    2. 数值分析双语教学与实践 (三类课程), 校级, 2014；

    3. 高等数值分析教学改革与实践, 校级, 2013. 

    荣誉：

    1. 2021年获校级研究生教学成果奖二等奖(排二)；

    2. 2018年获中泰国立奖教金二等奖；

    3. 2014年获威斯尼斯人60555入口官网教学奖励金二等奖；

    4. 2009年获新城科技园教学奖励金；

    5. 2007年获黑龙江省科学技术二等奖.


    研究生指导：

    硕士生在读6名：

    肖静婕（2021级）

    许铖镪（2021级）

    余韵（2022级）

    钟钇（2022级）

    李纯斌（2023级）

    陈静（2023级）


    博士生在读4名：

    李艳（2020秋博）

    王艺博（2021春博）

    邓楠（2022春博）

    何佳琴（2023秋博）


    博士后1名

    李胜悦（2023年11月进站）


    毕业9名：

    李胜悦（2018秋博、2022年6月毕业）威斯尼斯人60555入口官网 助理研究员 至善博士后

    徐秋红（2020级） 苏州开发区中学教师

    邓楠 （2019级硕）  威斯尼斯人60555入口官网读博

    朱美瑾（2018级硕） 河南省南阳市委（选调生）

    梁佳 （2016级硕）  北京市IT行业、机器学习／算法工程师

    赵景宝（2014级硕）  金陵中学仙林分校教师

    李学艳（2013级硕）  江苏省无锡市中学教师

    佟振光（2012级硕）  上海市IT行业、软件开发

    洪会粉（2012级硕）  威斯尼斯人60555入口官网数学系博士毕业、现为南京邮电大学副教授

    李秀萍（2011级硕）  首都经贸大学经济管理专业博士毕业、现为山东师范大学副教授

    郝朝鹏（2010级硕）  威斯尼斯人60555入口官网数学系博士毕业、美国伍斯特理工学院博士毕业、现为威斯尼斯人60555入口官网上岗研究员



  • 1. 本人为以下国际学术期刊的长期审稿人：


    Journal of Computational and Applied Mathematics

    Journal of Computational Physics

    Applied Mathematics and Computation

    Applied Mathematics Letters

    Applied Mathematical Modelling

    Applied Numerical Mathematics

    Computers and Mathematics with Applications

    Nonlinear Analysis: Hybrid Systems

    International Journal of Computer Mathematics


    2. 本人为中国仿真学会仿真算法专业委员会委员；江苏省工业与应用数学学会秘书长.