The field of numerical methods for conservation laws and radiative transfer is witnessing a significant shift towards the development of more robust and efficient algorithms. Researchers are focusing on improving the stability and accuracy of existing methods, such as semi-implicit multilevel spectral deferred correction (SI-MLSDC) methods and semi-Lagrangian discontinuous Galerkin methods. These advancements are crucial in simulating complex phenomena, including high-energy density physics and astrophysics. Notably, the development of energy-conserving methods and the use of high-order operator splitting strategies are leading to more accurate and stable numerical solutions. Furthermore, the investigation of new numerical methods, such as the Second Moment Method (SMM), is providing promising results in modeling thermal radiative transfer. Noteworthy papers include:

• A high-order energy-conserving semi-Lagrangian discontinuous Galerkin method for the Vlasov-Ampere system, which proposes a novel method that achieves high-order accuracy and unconditional stability.
• A study on the stability of the first-order unified gas-kinetic scheme based on a linear kinetic model, which provides a rigorous proof of the weighted L2-stability of the method.