Numerical simulation and convergence analysis for Riemann-Liouville fractional initial value problem involving weak singularity

Abstract

The present work considers a Riemann-Liouville fractional initial value problem (IVP) associated with homogeneous initial condition involving a weak singularity near the origin. Due to presence of initial singularity, an initial layer occurs at t = 0. The L1 scheme is introduced on a uniform mesh to approximate the solution. The convergence analysis shows that the present method is more accurate and produces less error compared to some existing methods on any subdomain away from the origin while the proposed method is comparable over the entire region. Numerical examples and comparison results are provided in order to show the effectiveness of the proposed method.