Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems

We consider a system of ℓ ≥ 2 one-dimensional singularly perturbed reaction-diffusion equations coupled at the zero-order term. The second derivative of each equation is multiplied by a distinct small parameter. We show how to decompose the solution to the problem into regular and layer parts. Properties of the discretized operator are established using discrete Green's functions. We prove that a central difference scheme on certain layer-adapted meshes converges independently of the perturbation parameters. Supporting numerical examples confirm our theoretical results.