  The inhomogeneous Zerilli equation is solved in time-domain numerically with
the Chebyshev spectral collocation method to investigate a radial-infall of the
point particle towards a Schwarzschild black hole. Singular source terms due to
the point particle appear in the equation in the form of the Dirac
$\delta$-function and its derivative. For the approximation of singular source
terms, we use the direct derivative projection method without any
regularization. The gravitational waveforms are evaluated as a function of
time. We compare the results of the spectral collocation method with those of
the explicit second-order central-difference method. The numerical results show
that the spectral collocation approximation with the direct projection method
is accurate and converges rapidly when compared with the finite-difference
method.
