A) 系统建立了扩展 WKB 渐近近似理论，证明了高斯光束近似的最优一阶精度。代表作：
[1] C. Zheng, J. Hu, Extended WKB analysis for the linear vectorial wave equation in the high-frequency regime, Commun. Comput. Sci., DOI: 10.4310/CMS.2020.v18.n3.a5, 2020.
[2] C. Zheng, Optimal error estimates for first-order Gaussian beam approximations to the Schrodinger Equation, SIAM J. Numer. Anal., 2014, 52(6), pp. 2905~2930.
B) 系统建立了广义积分方程方法的理论框架，适用于求解任何具有局部对称性的线性方程。代表作：
[3] J. Yin, C. Zheng, Space reduction for linear systems with local symmetry, J. Sci. Comput., DOI: 10.1007/ s10915-021-01663-0, 2021.
C) 系统地发展了非局部微分方程的人工边界方法。代表作：
[4] C. Zheng, Q. Du, X. Ma, J. Zhang, Stability and error analysis for a second-order fast approximation of the local and nonlocal diffusion equations on the real line, SIAM J. Numer. Anal., 2020, 58(3), pp. 1893-1917.
D) 发展了人工边界条件的快速算法及其理论。代表作：
[5] B. Li, J. Zhang, C. Zheng, An efficient second-order finite difference method for the one-dimensional Schrödinger equation with absorbing boundary conditions, SIAM J. Numer. Anal., DOI: 10.1137/17M1122347.
