This project consists of the development of numerical methods and mathematical. software for the solution of ordinary and partial differential equations that describe dynamic physiological processes. Many biological processes can be described by systems of ordinary or partial differential equations. Most, but not all, of these systems are nonlinear and often include multiple time scales i.e., there is a """"""""fast"""""""" in time phase, perhaps and intermediate phase, and a """"""""slow"""""""" or longer phase to show the complete behaviorial cycle of the process. Such systems are not easily or casually treatable by """"""""standard"""""""" numerical methods. This project is concerned with developing or adopting numerical solution methods that can apply to a wide class of such models and equations. In FY'92 versions of the PDEPGMS were converted to the """"""""C"""""""" language using the Bell Labs FORTOC system. Efforts to debug and recompile versions of the software are in progress. Preliminary studies were explored on adaptation of these methods for moving boundary problems with an application to acrosomal growth in cells. Further work in this area will concentrate on numerical methods to solve a moving boundary problem with an iterative refinement scheme.
