A posteriori error estimation in maximum norm for a two-point boundary value problem with a Riemann–Liouville fractional derivative

Abstract

A Riemann–Liouville two-point boundary value problem is considered. An integral discretization scheme is developed to approximate the Volterra integral equation transformed from the Riemann–Liouville boundary value problem. The stability results and a posteriori error analysis are given. A solution-adaptive algorithm based on a posteriori error analysis is designed by equidistributing arc-length monitor function. Numerical experiments are presented to support the theoretical result.