HIGHER ORDER APPROXIMATION DIFFERENCE SCHEME FOR TRANSPORT EQUATION

E.V. Diyankova, O.S. Shirokovskaya
VANT. Ser.: Mat. Mod. Fiz. Proc 1994. Вып.2. С. 17-21.

      The method of TVD-type for difference scheme generation is proposed. The obtained scheme is used for numerical solving of trasport equation and is constructed by adding antidiffusional fluxes to initial first order scheme.
      The scheme has a simple form. It is explicit conservative and third order approximating in the field of smooth solutions (except for extreme vicinities) on the uniform spatial grid.
      The simple algorithm for difference equation in the case of two spatial variables is proposed. It allows to conserve the scheme approximation order for commutative spatial operators.