Abstract
In last years, several problems about nonlinear computational stability have been studied. Many nonlinear computational unstable examples of Richtmyer-type and Fornberg-type are obtained. It is shown that the instability may occur for leap-frog Lilly’s scheme and leapfrog Arakawa’s scheme which are used in the meteorology and keep energy-conservation instantaneously. In Galerkin finite element model and spectral model with leap-frog time-difference, similar examples of nonlinear instability also exist. The general mechanisms of nonlinear computational instability are discussed, particularly the effects of initial conditions on the computational stability are analysed. Furthermore, some theorems on the sufficient conditions for computational stability have been proved and some schemes with non-negativity of numerical operator which can guarantee the nonlinear computational stability are given.
