The midpoint upwind scheme Original Research Article

A modified upwind scheme is considered for a singularly perturbed two-point boundary value problem whose solution has a single boundary layer. The scheme is analyzed on an arbitrary mesh. It is then analyzed on a Shishkin mesh and precise convergence bounds are obtained, which show that the scheme is superior to the standard upwind scheme. A variant of the scheme on the same Shishkin mesh is proved to achieve even better convergence behaviour.