1. 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;

2. 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);

3. 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;

4. 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).

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. 

1. 2018年获中泰国立奖教金二等奖；

2. 2014年获东南大学教学奖励金二等奖;

3. 2009年获新城科技园教学奖励金;

4. 2007年获黑龙江省科学技术二等奖.

硕士生在读2名：陈丽媛、朱美瑾

博士生在读2名：李胜悦、刘玉芬

毕业7名：

梁    佳  北京市IT行业 机器学习／算法工程师

赵景宝  金陵中学仙林分校教师

李学艳  江苏省无锡市中学教师

佟振光  南京市IT行业 软件开发

洪会粉  东南大学数学系博士生在读

李秀萍  首都经贸大学经济管理专业博士生在读

郝朝鹏  东南大学数学系博士生毕业、目前美国伍斯特理工学院博士在读

发表的学术论文：

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), pp. A1752–A1776, doi: 10.1137/140996495.

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, Applied Mathematical Modelling, 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. Maths. 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. Maths.,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. NGP_G-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. Maths. 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. Maths.,170 (2004), 255-268.

2. Jingjiu Zhao*, Wanrong Cao, Mingzhu Liu. Asymptotic stability of Runge-Kutta methods for the pantograph equations,J. Comput. Maths.,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：