ON THE TRUNCATION ERROR, STABILITY AND CONVERGENCE OF DIFFERENCE SOLUTIONS OF THE BAROTROPIC VORTICITY EQUATION

摘要

The truncation error, stability and convergence properties of various finite-difference formulations of the one-dimensional barotropic vorticity equation are considered, and analytic solutions of the difference equations for simple harmonic initial conditions are presented. Using conventional centered space differences, the schemes considered may be classified according to the method of time differencing as forward difference case unstable, the first-forward-then-centered difference case conditionally stable, and the implicit difference case unconditionally stable.