  A one-dimensional system of bosons interacting with contact and
single-Gaussian forces is studied with an expansion in hyperspherical
harmonics. The hyperradial potentials are calculated using the link between the
hyperspherical harmonics and the single-particle harmonic-oscillator basis
while the coupled hyperradial equations are solved with the Lagrange-mesh
method. Extensions of this method are proposed to achieve good convergence with
small numbers of mesh points for any truncation of hypermomentum. The
convergence with hypermomentum strongly depends on the range of the two-body
forces: it is very good for large ranges but deteriorates as the range
decreases, being the worst for the contact interaction. In all cases, the
lowest-order energy is within 4.5$\%$ of the exact solution and shows the
correct cubic asymptotic behaviour at large boson numbers. Details of the
convergence studies are presented for 3, 5, 20 and 100 bosons. A special
treatment for three bosons was found to be necessary. For single-Gaussian
interactions, the convergence rate improves with increasing boson number,
similar to what happens in the case of three-dimensional systems of bosons.
