Explicit three-point three-level FDMS for the one-dimensional constant-coefficient advection-diffusion equation

AbstractTwo highly stable explicit three-point three-level finite difference methods for the one-dimensional constant-coefficient advection-diffusion equation are described. These are developed using differencing on a (1,3,1) computational stencil. One is conditionally stable with second-order accuracy, the other is conditionally stable with third-order accuracy. Both are free of numerical diffusion. The two methods are compared, theoretically and by means of numerical experiments, with the leapfrog/Du Fort-Frankel (1,2,1) explicit method, the only three-level method currently employed to solve this equation. The former are generally found to be more accurate than the latter