The problem of construction of well-balanced schemes for hyperbolic systems of balance laws is considered. A method based on two sets of variables (conservative and equilibrium ones) is presented. We propose a method for the reconstruction of the equilibrium variables when the analytical mapping between the equilibrium variables and the conservative ones is unknown. For a model scalar equation, well-balanced schemes of up to the fourth order are constructed. Numerical results show the well-balanced properties and high order resolution of the schemes.
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