A Schwarz technique for a system of reaction diffusion equations with differing parameters. (English) Zbl 1181.65107

Stephens, Meghan; Madden, Niall

Hegarty, Alan F. (ed.) et al., BAIL 2008 – Boundary and interior layers. Proceedings of the international conference on boundary and interior layers – computational and asymptotic methods, Limerick, Ireland, July 28–August 1, 2008. Berlin: Springer (ISBN 978-3-642-00604-3/pbk; 978-3-642-00605-0/ebook). Lecture Notes in Computational Science and Engineering 69, 247-255 (2009).

Summary: We describe an overlapping Schwarz method for a coupled system of two singularly perturbed reaction-diffusion equations which may have differing perturbation parameters. We give an outline of the analysis that shows algorithm is parameter-uniform. Supporting numerical results are presented.
For the entire collection see [Zbl 1167.35002].

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations
34E15	Singular perturbations, general theory for ordinary differential equations

Keywords:

singular perturbation; overlapping Schwarz method; reaction-diffusion equations; numerical results