Domain Decomposition to Solve Transition Layers and Asymptotics

The author considers the numerical computation of stiff nonlinear partial differential equations (PDEs) that can be studied by the methods of singular perturbation. Two domain decomposition methods that solve numerically the layers of the singular perturbation problem are presented. These numerical methods use at different stages the information given by the asymptotic analysis. The simplified model of reacting flow of Majda [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 1059–1080], a singular perturbation problem with a turning point [L. Abrahamsson and S. Osher, SIAM J. Numer. Anal., 19 (1982), pp. 979–992], and a combustion problem [J. Pelaez, SIAM J. Appl. Math., 47 (1987), pp. 781–799] that models a sequence of two chemical reactions will be considered as test problems.