Three-Level Scheme for Solving the Radiation Diffusion Equation

A method for the numerical solution of a nonlinear equation describing the diffusion transfer of radiation energy has been developed. According to the method, the second time derivative with a small parameter is introduced into the parabolic equation and an explicit difference scheme is applied. The explicit approximation of the initial equation makes it possible to implement on its basis an algorithm that is effectively adapted to the architecture of high-performance computing systems. In comparison with the original scheme, the new one allows for a larger time integration step and a sufficiently high resolution of the solution structure, providing the second order of accuracy. A heuristic algorithm for choosing the parameters of the three-level difference scheme is proposed. A promising field of application of the method can be problems in plasma physics and astrophysics.