An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations (Q535464)

The authors consider the problem \[ -\varepsilon u''+ A u = f \quad \text{in} \quad\Omega=(0,1),\quad u(0)=a_{1},\quad u(1)= a_{2}, \] where \(f=(f_{1},f_{2},\dots,f_{M})^{T}, u=(u_{1}, u_{2},\dots,u_{M})^{T}\) and the elements of the matrix \(A\) satisfy special conditions such that exact the solution exists. Using the continuous Schwarz method and the decomposition of the domain \(\Omega\), they construct a discrete method to calculate an approximate solution of this problem.