Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Linear Instability of the Fifth-Order WENO Method
SIAM Journal on Numerical Analysis
Optimal implicit strong stability preserving Runge--Kutta methods
Applied Numerical Mathematics
Applied Numerical Mathematics
A Robust Reconstruction for Unstructured WENO Schemes
Journal of Scientific Computing
A low Mach number solver: Enhancing applicability
Journal of Computational Physics
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We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge---Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge---Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis.