Dynamical difference equations

Dynamical difference equations are motivated and developed. Conservation an d covariance laws are proved. Illustrative examples are described and discu ssed. Newtonian equations are stressed, but extensions to relativity and qu antum mechanics are indicated. The physical problem of convergence to the l imit as the time step goes to zero is shown to reveal an area in which quan tum mechanics and relativity are in disagreement. (C) 1998 Elsevier Science Ltd. All rights reserved.