A coupling difference scheme for the numerical solution of a singular perturbation problem (Q1209018)

This paper deals with the following singularly perturbed boundary value problem \(\varepsilon u''+b(x)u'-c(x)u=f(x)\), \(0<x<1\), \(u(0)=\mu_ 0\), \(u(1)=\mu_ 1\), where \(\varepsilon\) is a constant in (0,1], \(b(x)\), \(c(x)\), \(f(x)\in C^ 3[0,1]\) are given functions and \(b(x)>2\beta>0\), \(c(x)\geq 0\). The authors couple the central difference scheme and the Abrahamsson-Keller-Kreiss box scheme and get a uniformly second order convergent difference scheme. Some numerical results are provided.