THE PARAMETRIC "ROMB" SCHEME FAMILY FOR A 2-D HEAT CONDUCTION EQUATION

V.N. Pisarev
VANT. Ser.: Mat. Mod. Fiz. Proc 1992. Вып.3. С. 42-48.

      The parametric "Romb" scheme family is considered for a two-dimensional heat conduction equation. For some scheme parameter and difference mesh restrictions, approximation uncertainties, stability and convergence are investigated. The approximation Is studied for a heat conduction equation written in curvilinear coordinates in terms of normal heat flux components. The energy inequality method is used to prove stability and covergence. Equivalent schemes for temperatures are obtained on a diamond mesh. It is found that there is no schemes similar to those developed in this paper among well-known nine-point schemes.