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We present a theoretical method for solving the chemical evolution ofgalaxies, by assuming an instantaneous recycling approximation for chemicalelements restored by massive stars and the Delay Time Distribution formalismfor the delayed chemical enrichment by Type Ia Supernovae. The galaxy gas massassembly history, together with the assumed stellar yields and initial massfunction, represent the starting point of this method. We derive a simple andgeneral equation which closely relates the Laplace transforms of the galaxy gasaccretion history and star formation history, which can be used to simplify theproblem of retrieving these quantities in the galaxy evolution models assuminga linear Schmidt-Kennicutt law. We find that - once the galaxy star formationhistory has been reconstructed from our assumptions - the differential equationfor the evolution of the chemical element $X$ can be suitably solved withclassical 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, byassuming a decaying exponential infall rate of gas and different delay timedistributions for Type Ia Supernovae; we also explore the effect of assuming anonlinear Schmidt-Kennicutt law, with the index of the power law being $k=1.4$.Although approximate, we conclude that our model with the single degeneratescenario for Type Ia Supernovae provides the best agreement with the observedset of data. Our method can be used by other complementary galaxy stellarpopulation synthesis models to predict also the chemical evolution of galaxies.

A simple and general method for solving detailed chemical evolution with delayed production of iron and other chemical elements