A posteriori error estimation in maximum norm for a two-point boundary value problem with a Riemann–Liouville fractional derivative. (April 2020)

• Record Type: Journal Article
• Authors: Cen, Zhongdi; Liu, Li-Bin; Huang, Jian
• Is Part Of: Applied mathematics letters. Volume 102(2020)
• Publication Date: 2020-04
• Subjects: Riemann–Liouville fractional derivative -- Boundary value problem -- Grönwall inequality -- A posteriori error estimate; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106086
• Languages: English
• ISSNs: 0893-9659

Abstract

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.