EXAMINATION OF THE BEHAVIOR OF THE FULLY IMPLICIT FINITE-DIFFERENCE ALGORITHM WITH THE RICHTMYER MODIFICATION - BEHAVIOR WITH AN EXPONENTIALLY EXPANDING TIME GRID

This paper describes the development and application of the fully impl icit finite-difference algorithm with the Richtmyer modification (the FIRM algorithm) and an exponential time grid to simulations of stiff p roblems involving homogeneous kinetics and simulations of stiff proble ms involving semi-infinite linear diffusion coupled with heterogeneous and homogeneous kinetics. The accuracy and stability of the FIRM algo rithm with various levels and the dependence upon the starting protoco l are discussed in detail.