The weak nonlinear instability of Euler explicit scheme for the convective equation
The weak nonlinear instability of the Euler explicit difference schemes is considered for the one-dimensional nonlinear convective equation, where the field of velocity is subject to periodic boundary and initial conditions. The problem is studied analytically making use of perturbation expansion and discrete Fourier transform techniques. A short time weak nonlinear growth of Fourier modes for the error is found, provided that the linear stability conditions are satisfied and the maximum growth is approximately proportional to the inverse of the grid spacing.
scientific article; zbMATH DE number 4018283