UNCONDITIONAL STABILITY, MONOTONICITY AND ACCURACY OF THE LINEAR EXPONENTIAL INTERPOLATION FUNCTION FOR THE BURGERS-EQUATION

The linear exponential function used as an interpolant in the generati on of finite difference representations of convection-diffusion equati ons, is shown to possess several desirable properties not normally fou nd in representations derived from polynomials. These properties inclu de unconditional stability if used in implicit methods, nonoscillatory solutions without the use of flux limiters, and high accuracy. It is also shown that all of these properties are maintained to second-order if the function is used as a spline basis. Comparisons with a number of other schemes are given using the nonlinear Burgers equation. The w ork here provides the background for the functions arising from a new generalization of Roscoe's method which will be presented in another p aper. (C) 1998 Elsevier Science Ltd. All rights reserved.