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ON STABILITY OF TVDR DIFFERENCE SCHEMES FOR SOLUTION OF THE 1D RADIATION TRANSPORT EQUATION

A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.1. С. 16-28.

In computational physics, the transport equation is one of the fundamental equations widely accepted to describe the radiation gasdynamics processes. A lot of papers were devoted to the problem of developing numerical methods to solve the radiation transport equation. Nonlinear TVDR schemes of a higher approximation order (higher than the 1st order) constructed using the classic TVD methodology comprise a separate class of schemes. The paper describes the study of the TVDR difference scheme stability using the spectral Neumann criterion for 1D transport equation. The comparison between the stability of St and TVD schemes is presented. Conclusions concerning the stability conditions for TVD and TVDR schemes are made.

Keywords: transport equation, difference schemes, stability.








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