Numerical study of a nonlinear heat equation for plasma physics

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Abstract
This paper is devoted to the numerical approximation of a nonlinear parabolic balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical difficulties, in particular for the long-time behaviour approximation, when solved with standard methods. An efficient numerical scheme is presented in this paper, based on a combination of a directional splitting scheme and the implicit–explicit scheme introduced in Filbet and Jin [A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comput. Phys. 229 (2010), pp. 7625–7648].

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