Modified integral-factor method for steady convection-diffusion equations (Q1341223)

On the basis of the integral-factor method, a modified integral-factor method is presented. The following boundary value problem for steady convection-diffusion equation: \(\varepsilon y''+ f(x,y) y'+ g(x)y= s(x)\), \(a<x <b\), \(y(a)= \alpha\), \(y(b)= \beta\), \(\varepsilon\ll 1\), has been solved. The numerical results (even for large grid Peclet number) are non-oscillating and have second-order accuracy. Six typical examples with different cases are tested.