Analyses have been made of the truncation error for the following finite difference approximations to the eigenvalue and boundary value problems evolving from the one-group neutron diffusion equation: (i) The seven-point relation; (ii) The fifteen-point relation; (iii) The nineteen-point relation; and (iv) The twenty-seven point relation. These methods have been derived using a Taylor series expansion technique and applied to the Laplacian operator contained in that equation in (x,y,z) geometry for various reactor configurations and boundary conditions;It has been shown that for methods ii and iii, a 4th order truncation error can be achieved, whereas for the 27-point approximation, a 6th order truncation error is possible;From the computer results of sample problems, considerable savings in accuracy (accurate eigenvalue and/or eigenfunctions) and system memory (fewer number of meshes required) can be obtained using the high order approximations, especially the 27-point relation, as compared to the 2nd order approximation.