An efficient numerical method for a Riemann–Liouville two-point boundary value problem. (May 2020) - Huang, Jian; Cen, Zhongdi; Liu, Li-Bin; Zhao, Jialiang
Abstract: In this paper a numerical method is considered for a two-point boundary value problem with a Riemann–Liouville fractional derivative, where the exact solution may have weak singularity. The linear interpolation is used to approximate the functions in the fractional integral transformed from the Riemann–Liouville boundary value problem. In order to capture the singular phenomena of the exact solution, an adaptive mesh is developed by equidistributing a monitor function. The stability is derived by a modified Grönwall inequality. It is shown that the scheme is second-order convergent. Numerical experiments are provided to demonstrate the theoretical results.