孟祥云

博士、副教授

基本信息

办公电话： 电子邮件： xymeng1@bjtu.edu.cn
通讯地址： 邮编：

教育背景

2011.09 - 2016.07 北京大学，计算数学，直博

2007.09 - 2011.07 吉林大学，信息与计算科学，本科

工作经历

2021.01 至今 北京交通大学，副教授
2019.07 - 2020.12 北京交通大学，讲师
2018.09 - 2018.12 University of Limerick，访问学者
 2016.07 - 2019.07 中国工程物理研究院，博士后

研究方向

  • 计算数学
  • 应用数学

招生专业

  • 数学硕士

科研项目

国家自然科学基金项目、基本科研业务费项目等

教学工作

本科生课程：《数值计算》、《数学建模》、《几何与代数》、《复变函数与积分变换》等

研究生课程：《数值分析》、《有限元方法及其应用》等

论文/期刊

Selected publications:


  • Kopteva N, Meng X. Error analysis for a fractional-derivative parabolic problem on quasi-graded meshes using barrier functions, SIAM Journal on Numerical Analysis, 2020, 58(2): 1217-1238.

  • Meng X, Stynes M. Barrier function local and global analysis of an L1 finite element method for a multiterm time-fractional initial-boundary value problem. Journal of Scientific Computing, 2020, 84(1): 1-16.
  • Huang C, Liu X, Meng X, Stynes M. Error analysis of a finite difference method on graded meshes for a multiterm time-fractional initial-boundary value problem. Computational Methods in Applied Mathematics, 2020, 20(4): 815-825.
  • Ren H, Meng X, Liu R, Hou J, Yu Y. A class of improved fractional physics informed neural networks. Neurocomputing, 2023, 562: 126890.
  • Hou J, Yu Y, Wang J, Ren H, Meng X. Local analysis of L1-finite difference method on graded meshes for multi-term two-dimensional time-fractional initial-boundary value problem with Neumann boundary conditions. Computers and Mathematics with Applications, 2024, 157: 209-214.



  • Meng X, Stynes M. Balanced-Norm and Energy-Norm Error Analyses for a Backward Euler/FEM Solving a Singularly Perturbed Parabolic Reaction-Diffusion Problem. Journal of Scientific Computing, 2022, 92(2): 67.
  • Meng X, Stynes M. Balanced and energy norm error bounds for a spatial FEM with Crank-Nicolson and BDF2 time discretisation applied to a singularly perturbed reaction-diffusion problem. Numerical Algorithms, 2023: 1-22.



  • Meng X, Stynes M. Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions. Advances in Computational Mathematics, 2019, 45(2): 1105-1128.
  • Meng X, Stynes M. Uniform error analysis of a rectangular Morley finite element method on a Shishkin mesh for a 4th-order singularly perturbed boundary value problem. Submitted.



  • Wang Y, Meng X, Li Y. The finite volume element method on the shishkin mesh for a singularly perturbed reaction–diffusion problem. Computers and Mathematics with Applications, 2021, 84: 112-127.
  • Wang Y, Meng X, Li Y. The Bogner-Fox-Schmit Element Finite Volume Methods on the Shishkin Mesh for Fourth-Order Singularly Perturbed Elliptic Problems. Journal of Scientific Computing, 2022, 93(1): 4.
  • Wang Y, Li Y, Meng X. An upwind finite volume element method on a Shishkin mesh for singularly perturbed convection–diffusion problems. Journal of Computational and Applied Mathematics, 2023: 115493.
  • Meng X, Stynes M. Energy-norm and balanced-norm supercloseness error analysis of a finite volume method on Shishkin meshes for singularly perturbed reaction–diffusion problems. Calcolo, 2023, 60(40): 1-37.



  • Liu S, Meng X, Zhai Q. Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D. Journal of Computational and Applied Mathematics, 2025, 457: 116324.
  • Liu S, Meng X, Zhai Q. Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D. Advances in Applied Mathematics and Mechanics, 2025, 17, Accepted.



  • Meng X, Yang X, Zhang S. Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions. Science China Mathematics, 2016, 59: 2245-2264.



  • Meng X, Stynes M. The Green's function and a maximum principle for a Caputo two-point boundary value problem with a convection term. Journal of Mathematical Analysis and Applications, 2018, 461(1): 198-218.
  • Meng X, Stynes M. Green's functions, positive solutions, and a Lyapunov inequality for a Caputo fractional-derivative boundary value problem. Fractional Calculus and Applied Analysis, 2019, 22(3): 750-766.