A note on the computation of the outflow derivative for singular perturbation problems (Q1200227)

The author derives a method for computing the outflow derivative of the following singular perturbation problem \(-\varepsilon y''+a(x) y'+b(x)y=f(x)\) on \([0,P]\), \(y(0)=y_ 0\), \(y(P)=y_ 1\), where \(\varepsilon \ll 1\), and \(a(x)\), \(b(x)\) are \(C^ \infty\)-functions such that \(a(x)\neq 0\) for any \(0\leq x\leq P\). The method essentially involves integrating the differential equation numerically, and numerical experiments indicate the technique is very accurate when the problem is convection dominated.