Spline difference scheme and minimum principle for a reaction-diffusion problem

Katarina Surla, Ljiljana Tefanov, Zorica Uzelac

The linear singularly perturbed reaction-diffusion problem is considered. The spline difference scheme on the Shishkin mesh is used to solve the problem numerically. With the special position of collocation points, the obtained scheme satisfies the discrete minimum principle. Numerical experiments which confirm theoretical results are presented.