Nonlinear canonical midpoint splitting meshfree method with second-order accuracy for strongly stiff radiation diffusion problem

Radiation diffusion problems are typically stiff problems, arising from disparate scales among different physical quantities or the presence of transient rapid variations. This paper constructs a second-order accurate nonlinear canonical midpoint splitting meshfree (NCMSM) method. Combining with the radial basis functions (RBFs) collocation technique, the stiff (strongly stiff) and non-stiff (weakly stiff) subproblems are solved by the implicit midpoint method and generalized explicit midpoint method for temporal discretization respectively. The implicitly discretized equation is directly solved using the simplified Newton iteration method. The stability and convergence analyses are provided. The new method can flexibly adapt to irregular domains and yield high-precision effectiveness for 2D, 3D strongly stiff radiation diffusion problems. The experimental results of the proposed method are compared with the finite difference-based CES method (Li, 2016), CMS method (Liet al., 2025), and the NCESM method (Fenget al., 2026). The comparisons verify the feasibility and high precision of the NCMSM method.