Scroggs, Jeffrey S.; Sorensen, Danny C. An asymptotic induced numerical method for the convection-diffusion- reaction equation. (English) Zbl 0676.65102 Mathematics for large scale computing, Lect. Notes Pure Appl. Math. 120, 81-114 (1989). [For the entire collection see Zbl 0673.00019.] A new approach to solving time dependent reaction convection diffusion equation with small parameter on the diffusion term is discussed and demonstrated. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions were certain reduced equations may be solved in place of the full equation. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run-time results demonstrate the viability of the method. Reviewer: Hou Zongyi MSC: 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 65Y05 Parallel numerical computation 65H10 Numerical computation of solutions to systems of equations 35K57 Reaction-diffusion equations Keywords:time dependent reaction convection diffusion equation; small parameter; domain decomposition; singular perturbation Citations:Zbl 0673.00019 PDFBibTeX XML