A PARAMETRIC FAMILY OF ROMB SCHEMES FOR A 1-D HEAT CONDUCTION EQUATION

V. N. Pisarev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1986. Вып.2. С. 67-75.

      The paper studies a multiparameter family of ROMB schemes for a linear heat conduction equation. A parallel is drawn between the ROMB and three-point schemes. Equivalent three-point schemes are obtained both for temperatures and heat fluxes defined at mesh nodes. It is found that several well-known schemes belong to the parametric family of ROMB schemes. However, in some simplest cases the ROMB may be thought of as a weighted three-point scheme. Some issues concerning the underlying theory for this scheme are considered.