Modified-truncation finite difference schemes

A method is presented for modifying the truncation error of a given finite difference scheme approximating a nonlinear evolution equation. The new scheme has several advantages over the original. It is higher order, in the absence of time derivatives, has the same time-step requirements, it removes nonphysical oscillations, and it is not less accurate than the original scheme. The idea applied to a finite difference scheme approximating a geophysical flow produces a scheme consistent with the accuracy of the original scheme, but on a mesh three times more refined.