A Comparison of Numerical Methods for Solving Diffusion-Reaction Equations in Air Quality Models

In this paper we analyze the efficiency of some stiff ode solvers, applied to the coupled solution of vertical turbulent diffusion and chemical kinetics in Air Quality Models. We consider four general-purpose solvers, based on bdf or Rosenbrock methods, and two special-purpose solvers, developed for odes from atmospheric chemistry, and compare their performance on three test problems using different chemical models. The general-purpose solvers have been modified to take advantage of the sparsity of the Jacobian matrices arising in the application of implicit methods. The obtained results show that general-purpose solvers, provided with suitable sparse matrix techniques, perform generally better than special-purpose ones. Our analysis extends to the diffusion-reaction equations the recent work of other research groups, comparing ode solvers on atmospheric chemical kinetics equations.