Abstract: To improve the robustness and convergence speed of the Newton method and Picard method of solving radiation diffusion equations, several work is introduced when they are used to solve the three temperature radiation diffusion equation system, including the selection of initial iteration value, the treatment of physical constraints in the iterative process, the combination of the Picard iterative method and Anderson acceleration, and the improvement of Anderson acceleration method. By applying application-driven treatments and improvements, the two methods can be used to solve the nonlinear radiation diffusion equations.