Two previously derived approximations to the linear-linear nodal transport method, the linear-nodal (LN) and the linear-linear (LL) methods, are reexamined, together with a new approximation, the bilinear (BL) method, that takes into account the bilinear nodal flux moment. The three methods differ in the degree of analyticity retained in the final discrete variable equations; however, they all possess the very high accuracy characteristic of nodal methods. Unlike previous work, the final equations are manipulated and cast in the form of the classical weighted diamond-difference (WDD) equations (not just a WDD algorithm). This makes them simple to implement in a computer code, especially for those users who have experience with WDD algorithms. Other algorithms, such as the nodal algorithm, also can be used to solve the WDD-form equations. A computer program that solves two-dimensional transport problems using the LN, LL, or the BL method is used to solve three test problems. The results are used to confirm our algebraic manipulations of the nodal equations and also to compare the performance of the three methods from the computational, as well as the theoretical, point of view. The three methods are found to have comparable accuracies for the problems studied, especially on meshes that are sufficiently fine.