  We describe the determination of the longitudinal structure function $F_{L}$
at NLO and NNLO approximations, using Laplace transform techniques, into the
parametrization of $F_{2}(x,Q^{2})$ and its derivative with respect to
$\ln{Q^{2}}$ at low values of the Bjorken variable $x$. The obtained results
are comparable with others by considering the effect of the charm quark mass to
the longitudinal structure function, which leads to rescaling variable for
$n_{f}=4$. Numerical calculations and comparison with H1 data demonstrate that
the suggested method provides reliable $F_{L}(x,Q^{2})$ at small $x$ in a wide
range of $Q^{2}$ values and can be applied as well in analyses of ultra-high
energy processes with cosmic neutrinos. The obtained longitudinal structure
functions with and without the LHeC simulated uncertainties
[CERN-ACC-Note-2020-0002, LHeC Collaboration and FCC-he Study Group, P.
Agostini et al., J. Phys. G: Nucl. Part. Phys. {\bf48}, 110501(2021).] are
compared with the H1 Collaboration data [Eur.Phys.J.C{\bf74}, 2814(2014) and
Eur.Phys.J.C{\bf71}, 1579 (2011)] and with the results from CT18
[Phys.Rev.D{\bf103}, 014013(2021)] parametrization model at NLO and NNLO
approximations.
