Improvement of numerical solution by boundary value technique for singularly perturbed one dimensional reaction diffusion problem. (Q1399750)

The class of singularly perturbed boundary value problems considered is: \[ -\varepsilon^2u''(x)+b(x)u(x)=f(x),\; x\in (0,1),\;u(0)=A,\;u(1)=B \] where \(b, f\) are assumed to be smooth functions, \(b(x)\geq b_0\) on \([0,1]\) for some \(b_0>0\) and \(\epsilon\) is small. The boundary value technique considered involves dividing the domain of the equation into three non-overlapping subdomains and solving the equation separately as three two-point boundary value problems. A fitted operator method is used on an inner region and standard central difference methods are used on the outer regions. Error estimates are derived and several numerical experiments are reported.