The length factor artificial neural network method (LFANNM) has been demonstrated as an alternative to the finite element method for solving boundary values problems (BVPs). Besides optimizing on a rectangular grid rather than the typical triangular mesh of the FEM, a primary advantage of the LFANNM is that the resulting continuous approximate solution eliminates the need for interpolation between grid points. This manuscript compares the accuracy of the LFANNM and FEM for BVPs with known analytical solutions, both for single partial differential equations (PDEs) and for coupled systems of PDEs. Unlike the FEM, results show that error for the LFANNM on and between grid points is roughly equivalent. This superior built-in interpolation allows the LFANNM to outperform the FEM in most cases even when trained with as much as an order of magnitude fewer nodal points.