This investigation is directed towards the development of robust, efficient numerical methods and software for solving large stiff systems of ordinary differential equations. Of particular interest are systems that result from the semi-discretization of parabolic and mixed type partial differential equations, for example, the equations that model reaction diffusion convection processes. The effort will require the development of preconditioned iterative methods for large structured systems of linear and nonlinear algebraic equations. Algorithms and software will be designed to take advantage of shared memory multiprocesor/vector computer hardware. Moreover, algorithms and software will be suitable for use on a wide range of computers. The effort if successful will provide mathematical software that will facilitate computer modelling and simulation in various scientific and engineering fields. The numerical methods and software developed will extend the capability to solve an important class of partial differential equations.
