An Implicit-Explicit Hybrid Solver for a System of Stiff Kinetic Equations

A new stiff ordinary differential equation solver has been devised that separates the unknown variables into a fast group and a slow group. The fast variables are solved using the implicit backward-differentiation formulas but with a Jacobian of much smaller dimension than that of the original stiff system. The slow variables are solved using a simple explicit Adams-Bashforth scheme. The method, applied to a stiff atmospheric chemical system, yields an accuracy in the solution comparable to that of the commonly-used LSODE method at a relative tolerance level of 10-3 and an absolute tolerance level of 10-7 ppm, with one-third the execution time of LSODE. The method can be further fine-tuned to optimize its accuracy and execution time. As it is, the method should be an excellent candidate for the chemistry solver in air quality, combustion, and reactive flow models.