A simple and general method for solving detailed chemical evolution with
  delayed production of iron and other chemical elements
  We present a theoretical method for solving the chemical evolution of
galaxies, by assuming an instantaneous recycling approximation for chemical
elements restored by massive stars and the Delay Time Distribution formalism
for the delayed chemical enrichment by Type Ia Supernovae. The galaxy gas mass
assembly history, together with the assumed stellar yields and initial mass
function, represent the starting point of this method. We derive a simple and
general equation which closely relates the Laplace transforms of the galaxy gas
accretion history and star formation history, which can be used to simplify the
problem of retrieving these quantities in the galaxy evolution models assuming
a linear Schmidt-Kennicutt law. We find that - once the galaxy star formation
history has been reconstructed from our assumptions - the differential equation
for the evolution of the chemical element $X$ can be suitably solved with
classical methods. We apply our model to reproduce the [O/Fe] and [Si/Fe] vs.
[Fe/H] chemical abundance patterns as observed at the solar neighborhood, by
assuming a decaying exponential infall rate of gas and different delay time
distributions for Type Ia Supernovae; we also explore the effect of assuming a
nonlinear Schmidt-Kennicutt law, with the index of the power law being $k=1.4$.
Although approximate, we conclude that our model with the single degenerate
scenario for Type Ia Supernovae provides the best agreement with the observed
set of data. Our method can be used by other complementary galaxy stellar
population synthesis models to predict also the chemical evolution of galaxies.
