The field of numerical methods for differential equations and stochastic processes is rapidly advancing, with a focus on developing innovative and efficient algorithms for solving complex problems. Recent research has centered on improving the convergence and stability of numerical methods, particularly in the context of non-linear and non-globally Lipschitz systems. Notable developments include the analysis of splitting methods for operator-valued differential Riccati equations, the investigation of strong and weak convergence orders of numerical methods for stochastic differential equations driven by time-changed Lévy noise, and the establishment of uniform-in-time weak error estimates for explicit full-discretization schemes for stochastic partial differential equations. Additionally, researchers have explored the application of novel numerical techniques, such as the random grid technique, to achieve high-order weak approximations for the Cox-Ingersoll-Ross process and the log-Heston process. The use of non-quadratic convex cost functions, such as Bregman divergence, has also been investigated in the context of linear quadratic regulators. Noteworthy papers include: the analysis of Lie and Strang splitting for operator-valued differential Riccati equations, which provides a rigorous convergence analysis in the infinite-dimensional setting; the investigation of strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise, which establishes the strong convergence order of 1/2 and weak convergence order of 1; and the development of high-order weak approximations for the Cox-Ingersoll-Ross process using the random grid technique, which achieves convergence of any order for smooth test functions.