@article{Wang2007LinearIO,
title={Linear Instability of the Fifth-Order WENO Method},
author={Rong Wang and Raymond J. Spiteri},
journal={SIAM J. Numerical Analysis},
year={2007},
volume={45},
pages={1871-1901}
}

The weighted essentially nonoscillatory (WENO) methods are popular spatial discretization methods for hyperbolic partial differential equations. In this paper we show that the combination of the widely used fifth-order WENO spatial discretization (WENO5) and the forward Euler time integration method is linearly unstable when numerically integrating hyperbolic conservation laws. Consequently it is not convergent. Furthermore we show that all two-stage, second-order explicit Runge–Kutta (ERK… CONTINUE READING