  The solution of a radial Schr\"odinger equation for {\psi}(r) containing a
nonlocal potential of the form \int{K(r,r') {\psi}(r') dr'} is obtained to high
accuracy by means of two methods. An application to the Perey-Buck nonlocality
is presented, without using a local equivalent representation. The first method
consists in expanding {\psi} in a set of Chebyshev polynomials, and solving the
matrix equation for the expansion coefficients numerically. An accuracy of
between 1:10^{6} to 1:10^{14} is obtained, depending on the number of
polynomials employed. The second method consists in expanding {\psi} into a set
of N Sturmian functions of positive energy, supplemented by an iteration
procedure. For N=15 an accuracy of 1:10^{4} is obtained without iterations.
After one iteration the accuracy is increased to 1:10^{6}. The method is
applicable to a general nonlocality K.
