A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems

A 2nd-order, L-stable Rosenbrock method from the eld of sti ordinary di erential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective and turbulent di usive transport. Partial di erential equation problems of this type occur in the eld of air pollution modelling. The focal point of the paper is to examine the Rosenbrock method for reliable and e cient use as an atmospheric chemical kinetics box-model solver within Strang-type operator splitting. In addition two W-method versions of the Rosenbrock method are discussed. These versions use an inexact Jacobian matrix and are meant to provide alternatives for Strang-splitting. Another alternative for Strang-splitting is a technique based on so-called source-splitting. This technique is brie y discussed. 1991 Mathematics Subject Classi cation: Primary: 65M06 and 65M20. Secondary: 65Y05 and 65Y20. 1991 Computing Reviews Classi cation System: G.1.8 and G.1.1, J.2.