Asymptotic initial value methods for two-parameter singularly perturbed boundary value problems for second order ordinary differential equations. (Q1406108)

Numerical methods are presented for solving two-parameter singular perturbed boundary value problems (BVPs) of the form \[ -\varepsilon y''(x)- \mu a(x) y'(x)+ b(x) y(x)= f(x),\quad x\in (0,1), \] \(y(0)= p\), \(y(1)= q\). The idea of these methods is to deduce initial value problems and/or terminal value problems from this BVP and then solve these problems numerically. The authors not only present the numerical methods but also the necessary theory, which includes stability results and error estimates. Two examples are given to illustrate them.