The field of numerical methods for partial differential equations is witnessing significant developments, with a focus on improving the accuracy and efficiency of existing methods. Researchers are exploring new approaches to tackle complex problems, such as multiscale parabolic equations, singularly perturbed coupled systems, and relativistic charged-particle dynamics. Noteworthy papers in this area include: A concurrent global-local numerical method for multiscale parabolic equations, which improves macroscopic and microscopic errors. An efficient spline-based scheme on Shishkin-type meshes for solving singularly perturbed coupled systems with Robin boundary conditions, achieving almost second-order convergence. Error and long-term analysis of two-step symmetric methods for relativistic charged-particle dynamics, which preserves energy, mass shell, and phase-space volume. A novel time integration scheme for linear parabolic PDEs, enhancing the Crank-Nicolson method with radial basis function interpolation for higher-order temporal accuracy.