  We investigate X-ray bursts during the thermal evolution of an accreting
neutron star which corresponds to the X-ray burster GS\ 1826-24. Physical
quantities of the neutron star are included using an equation of state below
and above the nuclear matter density. We adopt an equation of state and
construct an approximate network that saves the computational time and
calculates nuclear energy generation rates accompanying the abundance
evolutions. The mass and radius of the neutron star are got by solving the
stellar evolution equations from the center to the surface which involve
necessary information such as the nuclear energy generation in accreting
layers, heating from the crust, and neutrino emissions inside the stellar core.
We reproduce the light curve and recurrence time of the X-ray burst from GS
1826-24 within the standard deviation of 1$\sigma$ for the assumed accretion
rate, metallicity, and equation of state. It is concluded that the observed
recurrence time is consistent with the theoretical model having metallicity of
the initial CNO elements $Z_{\rm CNO}$ = 0.01. We suggest that the nuclear
reaction rates responsible for the $rp$-process should be examined in detail,
because the rates may change the shape of the light curve and our conclusion.
