| Abstract: |
| We propose a highly efficient second-order numerical scheme for approximating the long-time dynamics of a class of finite-dimensional nonlinear models arising in geophysical fluid dynamics. The method is unconditionally stable and requires solving only a fixed symmetric positive definite linear system at each time step. We prove that the numerical solutions remain uniformly bounded for all time and that the scheme accurately captures the long-time behavior of the underlying system. In particular, the global attractors and invariant measures of the scheme converge to those of the original model as the time step approaches zero. Numerical experiments on the Lorenz-96 system demonstrate that the scheme efficiently approximates long-time statistical properties and captures the invariant measures of the system. |
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