ON THE STABILITY OF A STABILIZING CORRECTION SCHEME WITH CENTRAL DIFFERENCES FOR SPATIAL VARIABLES IN THE 3D TRANSPORT EQUATION

It is generally accepted that the stabilizing correction scheme with central differences for spatial variables in the 3D transport equation is conditionally stable. The work shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and the magnitude of their increments rapidly approach zero as the Courant parameter tends to zero, allowing successful use of this scheme. Therefore, it is more accurate to refer to this scheme as practically conditionally stable.

stability of finite-difference schemes in multidimensional cases, fractional step method, stabilizing correction scheme, hyperbolic equations