The field of numerical methods for partial differential equations is witnessing significant advancements, driven by the development of innovative algorithms and techniques. One notable trend is the increasing focus on high-order methods, which offer improved accuracy and efficiency in solving complex problems. Researchers are exploring new approaches to address the challenges associated with these methods, such as the development of optimal solvers for the Helmholtz equation and the creation of efficient preconditioners for mixed finite element discretizations. Moreover, the integration of distributed computing and model order reduction techniques is enabling the solution of large-scale problems with unprecedented speed and accuracy. Noteworthy papers in this area include: An Optimal O(N) Helmholtz Solver for Complex Geometry using WaveHoltz and Overset Grids, which presents a highly efficient solver for the Helmholtz equation. Higher-order meshless schemes for hyperbolic equations, which introduces a new MUSCL-like meshless scheme with improved stability and accuracy. Mixed-Precision in High-Order Methods: the Impact of Floating-Point Precision on the ADER-DG Algorithm, which explores the effects of mixed precision on the accuracy of high-order discontinuous Galerkin methods.