Spline collocation methods for fractional differential equations: theoretical and computational aspects

Spline collocation methods are a powerful tool to discretize fractional differential equations, since they have a high order of convergence and strong stability properties. In this talk, we illustrate the convergence and stability analysis of one and two step spline collocation methods. We pay attention also to the efficient implementation of these methods, which requires the evaluation of fractional integrals. Some numerical experiments are provided to confirm theoretical results and to compare one and two step collocation methods. This is a joint work with B. Paternoster and D. Conte.