Research On The Evolutionary Equation And Its Numerical Stability Of The Mesoscale Nonlinear Gravitational Wave

In this paper, we study nonlinear perturbation analysis of mesoscale verticalcirculation and evolution equation by means of f plane, non-hydrostatic balance andfilter model. Outstanding nonlinear characteristic of mesoscale disturbance invertical direction, we obtain nonlinear symmetric disturbance equation anddisturbance amplitude's evolution equation by use of multi-scale and singularperturbation technique. The equation is an extensive Schr(o|¨)dinger one. Then by useof finite difference scheme, we get the solution of the extensiveSchr(o|¨)dinger equation, and then we try to prove the stability of the finite differencescheme and estimate the solution.