AbstractA residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one‐dimensional transport problem and (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term‐by‐term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual m