High-precision meshfree methods based on various linearization methods for 3D equilibrium radiation diffusion problem in complex domains

For 3D strongly nonlinear equilibrium radiation diffusion equation, a kind of new meshfree iteration methods based on Richtmyer, factorization, and Newton linearization techniques in complex domains is provided. The new methods avoid the difficulty of mesh generation while ensuring high accuracy. Through specific numerical experiments, it is shown that the new methods have good approximation performance for solving 3D strongly nonlinear problems in complex domains, and all achieve good precision with iteration counts of 2 nearly under the given parameters. The comparison between finite element method (FEM) with the presented methods shows that our new methods match with FEM when the time step is relatively small, but avoid mesh generating.