Neither method allows for anisotropy as published. Vidale's method is based directly on plane wave propagation, and so adding anisotropy to that algorithm is trivial. (In practice it is not so simple, because the oddly-shaped computational fronts in his method make error analysis difficult.)
We will analyze the derivation of Van Trier and Syme's method and show how their method is based on the isotropic dispersion relation. It is then a simple matter to recast their algorithm to use an anisotropic dispersion relation.
For these preliminary results, we use the two-step Lax-Wendroff finite-difference method instead of the upwind method presented in their paper.