Three-Layer Scheme for Solving the Radiation Diffusion Equation

Abstract

A method has been developed for the numerical solution of a nonlinear equation describing the diffusion transfer of radiation energy. The method is based on the introduction of the second time derivative with a small parameter into the parabolic equation and an explicit difference scheme. 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. The new scheme provides, in comparison with the original scheme, a larger time integration step and a sufficiently high resolution quality of the solution structure, providing the second order of accuracy. A heuristic algorithm for choosing the parameters of a three-layer difference scheme is proposed. A promising field of application of the method can be problems of plasma physics and astrophysics.