FINITE-DIFFERENCE SCHEMES FOR LONG-TIME INTEGRATION

A general method for constructing finite difference schemes for longti me integration problems is presented. It is demonstrated for discretiz ations of first and second space derivatives; however, the approach is not limited to these cases. The schemes are constructed so as to mini mize the global truncation error, taking into account the initial data . The resulting second-order compact schemes can be used for integrati on times fourfold or more longer than previously studied schemes with similar computational complexity. A similar approach was used to obtai n improved integration schemes. (C) 1994 Academic Press, Inc.