  We investigate the mesonic light-front bound-state equations of the 't Hooft
and Schwinger model in the two-particle, i.e. valence sector, for small fermion
mass. We perform a high precision determination of the mass and light-cone wave
function of the lowest lying meson by combining fermion mass perturbation
theory with a variational approach. All calculations are done entirely in the
fermionic representation without using any bosonization scheme. In a
step-by-step procedure we enlarge the space of variational parameters. For the
first two steps, the results are obtained analytically. Beyond that we use
computer algebraic and numerical methods. We achieve good convergence so that
the calculation of the meson mass squared can be extended to third order in the
fermion mass. Within the numerical treatment we include higher Fock states up
to six particles. Our results are consistent with all previous numerical
investigations, in particular lattice calculations. For the massive Schwinger
model, we find a small discrepancy (less than 2 percent) in comparison with
known bosonization results. Possible resolutions of this discrepancy are
discussed.
