The field of numerical methods for complex systems is experiencing significant growth, with a focus on developing efficient and robust algorithms for solving various types of equations. Recent developments have centered around improving the accuracy and stability of numerical methods, particularly for problems involving singularities, non-selfadjoint operators, and complex symmetric systems. Notable advancements include the development of adaptive multilevel preconditioned methods, sharp stability results for ascent-descent spectra, and new Rosenbrock-type methods for differential algebraic equations. Additionally, researchers have proposed innovative iteration methods and preconditioners for complex symmetric linear systems, as well as energy-conserving Hamiltonian boundary value methods. These advancements have the potential to significantly impact various fields, including physics, engineering, and computer science. Noteworthy papers include:

• Local Multilevel Preconditioned Jacobi-Davidson Method for Elliptic Eigenvalue Problems on Adaptive Meshes, which proposes an efficient adaptive multilevel preconditioned method with optimal computational complexity.
• Sharp Ascent-Descent Spectral Stability under Strong Resolvent Convergence, which establishes sharp stability results for non-selfadjoint operators.
• Rodas6P and Tsit5DA, which present two new Rosenbrock-type methods for solving index-1 differential algebraic equations.
• Lopsided HSS Iterative Method and Preconditioner for a class of Complex Symmetric Linear System, which proposes a new iteration method and preconditioner for complex symmetric linear systems.
• Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods, which develops energy-conserving Hamiltonian boundary value methods for Hamiltonian systems.