Maintaining the stability of a leapfrog scheme in the presence of source terms

The instability encountered by applying the upwind leapfrog method to the advection equation having a source term is resolved. The source term is eliminated by transforming the governing equation. Two types of transformation are examined and the method of the space transformation leads to a stable and accurate scheme for the one-dimensional advection equation. The method is also extended to the twodimensional acoustic equations in polar co-ordinates.