Convergence of dynamic iteration methods for initial value problems
SIAM Journal on Scientific and Statistical Computing
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Gauss-Seidel iteration for stiff odes from chemical kinetics
SIAM Journal on Scientific Computing
Explicit methods for stiff ODEs from atmospheric chemistry
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
On the convergence of operator splitting applied to conservation laws with source terms
SIAM Journal on Numerical Analysis
A stiff ODE preconditioner based on Newton linearization
Applied Numerical Mathematics
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Atmospheric chemistry transport (CT) models are vital in performing research on atmospheric chemical change. Even with the enormous computing capability delivered by massively parallel systems, many extended three-dimensional global CT simulations are not computationally feasible. The major obstacle in an atmospheric CT model is the nonlinear ordinary differential equation (ODE) system describing the chemical kinetics in the model. These ODE systems are usually stiff and can account for a significant portion of the total CPU time required to run the model. In this report, we describe a simple explicit algorithm useful in treating chemical ODE systems. This algorithm is one of a growing number of preconditioned time-stepping procedures based on dynamic iteration. In this study, the algorithm is compared with an established, general-purpose implementation of the common backward differentiation formulas. It is shown to be a viable choice for the chemical kinetics in a full 3-D atmospheric CT model across architectural platforms and with no special implementation.