Fitted mesh method for singularly perturbed reaction-convection-diffusion problems with boundary and interior layers (Q854409)

The authors propose a robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term. Theoretical bounds are derived for the derivatites of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Numerical examples are also provided to illustrate the convergence of the numerical approximations.