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

Authors: Sudarshan Santra; Jugal Mohapatra

Addresses: Department of Mathematics, National Institute of Technology Rourkela, Odisha, 769008, India ' Department of Mathematics, National Institute of Technology Rourkela, Odisha, 769008, India

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.

Keywords: Riemann-Liouville fractional IVP; Caputo derivative; L1 scheme; error analysis; weak singularity; existence uniqueness; finite difference; experimental evidence.

DOI: 10.1504/IJCSM.2023.135045

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.4, pp.340 - 349

Accepted: 07 Mar 2023
Published online: 28 Nov 2023 *

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