  The generalized pseudospectral method is employed to calculate the bound
states of Hulth\'en and Yukawa potentials in quantum mechanics, with special
emphases on higher excited states and stronger couplings. Accurate energy
eigenvalues, expectation values and radial probability densities are obtained
through a nonuniform and optimal spatial discretization of the radial
Schr\"odinger equation. Results accurate up to thirteen to fourteen significant
figures are reported for all the 55 eigenstates of both these potentials with
$n\leq$10 for arbitrary values of the screening parameters covering a wide
range of interaction. Furthermore, excited states as high as up to $n=17$ have
been computed with good accuracy for both these potentials. Excellent agreement
with the available literature data has been observed in all cases. The $n>6$
states of Yukawa potential has been considerably improved over all other
existing results currently available, while the same for Hulth\'en potential
are reported here for the first time. Excepting the $1s$ and $2s$ states of
Yukawa potential, the present method surpasses in accuracy all other existing
results in the stronger coupling region for all other states of both these
systems. This offers a simple and efficient scheme for the accurate calculation
of these and other screened Coulomb potentials.
