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Many applications involve partial differential equations which admits steady state solutions. The design of schemes which are able to correctly these equilibrium states may be challenging for numerical, in particular for high order ones. In this paper, inspired by-macro decomposition methods for kinetic equations, we present a class of which are capable to preserve the steady state solution and achieve order accuracy for a class of time dependent partial differential including nonlinear diffusion equations and kinetic equations. to systems of conservation laws with source terms are also discussed.
Pareschi et al. (Mon,) studied this question.
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