A new relaxation scheme for solving one-dimensional systems of conservation laws is presented in this paper. This scheme is based on combining a mapped weighted essentially nonoscillatory (WENO) reconstruction with relaxation approximation method proposed by Jin and Xin. The time discretization is implemented by an implicit-explicit Runge-Kutta method. The presented scheme is applied to the one-dimensional Euler equations subject to different initial data. The results demonstrate that our scheme has high accuracy and high-resolution properties.
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