Local and global manifolds in stiff reaction-diffusion systems

Publisher Summary This chapter examines two different approaches for constructing low-dimensional manifolds from a stiff system of reaction-diffusion partial differential equations (PDEs). They account for the fast time scales because of the reaction term or the interaction of the reaction and diffusion terms. The advantages and disadvantages of implementing these two approaches for the simplification of large and stiff systems of PDEs are discussed. The effects of diffusion in the shape of the manifold are examined with Computational Singular Perturbation from two approaches: the local and the global. The first approach is based on the original form of PDEs.