  This hybrid method (FE-DVR), introduced by Resigno and McCurdy, Phys. Rev. A
62, 032706 (2000), uses Lagrange polynomials in each partition, rather than
"hat" functions or Gaussian functions. These polynomials are discrete variable
representation functions, and are.orthogonal under the Gauss-Lobatto quadrature
discretization approximation. Accuracy analyses of this method are performed
for the case of a one dimensional Schroedinger equation with various types of
local and nonlocal potentials for scattering boundary conditions. The accuracy
is ascertained by comparison with a spectral Chebyshev integral equation
method, accurate to 1:10^(-11). For an accuracy of the phase shift of 1:10^(-8)
The FE-DVR method is found to be 100 times faster than a sixth order finite
difference method (Numerov), is easy to program, and can routinely achieve an
accuracy of better than 1:10^(-8) for the numerical examples studied.
