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 two-dimensional acoustic equations in polar co-ordinates. Copyright © 2003 John Wiley & Sons, Ltd.
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