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Two-dimensional three-temperature radiation diffusion equations coupled with the temperatures of photon, electron and ion are widely used in the numerical research of laser-driven implosion in inertial confinement fusion experiments. The equations describe the radiation evolution of electron, ion and photon among various materials. So they have strong nonlinearity and are built on complicated computational domains. Traditional numerical methods such as finite difference method and finite element method rely on meshes for discretization. In this paper, two types of meshfree methods based on radial basis function are proposed to solve two-dimensional three-temperature radiation diffusion equations. The first is using direct linearization of the diffusion term on each time layer and using non-symmetric collocation method combined with the compactly supported radial basis function on space. The second is using non-symmetric collocation method on space but constructing a successive permutation iteration algorithm with fully implicit scheme on each time layer. By comparing different linearization methods, we can find that successive permutation iteration algorithm is more effective. Accurate performance of the proposed methods are confirmed by a large number of numerical experiments. [ABSTRACT FROM AUTHOR]