Discussion: “Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures” (Newell, M. E., and Schmidt, F. W., 1970, ASME J. Heat Transfer, 92, pp. 159–167)

A direct solution method was used, for the solution of the set of difference equations, requiring only the storage of those elements contained between the two outermost nonzero diagonals of the coefficient matrix. The method used involves the triangular decomposition of the coefficient matrix followed by the solution of two triangular systems. Hounding errors present in t he first solution are then reduced to negligible proportions by an iterative method. The theory is as follows. Each set of equations may be written in the form