Abstract <p>The dissipative-dispersion properties of a third-order accurate projection-characteristic method designed for the numerical solving of the advection equation are examined. The scheme is referred to as Cubic Polynomial Projection (CPP) and is constructed using the grid-characteristic method with Hermite interpolation. The properties of the scheme are compared with those of the Cubic Interpolation Polynomial (CIP) scheme, which is widely used in computational practice and is also based on Hermite interpolation. Both schemes are characteristic ones, which is important for the transport of particles and explicit account of the exponential dependence of the solution on the optical width. Instead of the conventional interpolation closure typical for CIP, the CPP scheme uses orthoprojector closure. As a result, the scheme can be adapted to unstructured tetrahedral meshes and the difficulty of characteristics coplanar with cell faces can be circumvented, but the required memory resources are doubled even in the simplest one-dimensional case. It is shown that the projection cl-osure significantly improves the already fairly good dissipative-dispersion properties of the CIP&#xa0;scheme, bringing them significantly closer to the dissipative-dispersion properties of the exact solution of the advection equation. These conclusions are confirmed by numerical examples.</p>