Affiliations 

  • 1 Department of Mathematics, University of Sargodha, Sargodha, Pakistan
  • 2 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamil Nadu, India
  • 3 Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia
  • 4 School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia
PLoS One, 2024;19(5):e0296909.
PMID: 38753667 DOI: 10.1371/journal.pone.0296909

Abstract

The time fractional Schrödinger equation contributes to our understanding of complex quantum systems, anomalous diffusion processes, and the application of fractional calculus in physics and cubic B-spline is a versatile tool in numerical analysis and computer graphics. This paper introduces a numerical method for solving the time fractional Schrödinger equation using B-spline functions and the Atangana-Baleanu fractional derivative. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while a θ-weighted scheme is used to discretize the space directions. The efficiency of the method is demonstrated through numerical results, and error norms are examined at various values of the non-integer parameter, temporal directions, and spatial directions.

* Title and MeSH Headings from MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine.