An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions

Afzaal Mubashir Hayat, Muhammad Abbas, Homan Emadifar, Ahmed S M Alzaidi, Tahir Nazir and Farah Aini Abdullah

PLOS ONE, 2024, vol. 19, issue 5, 1-24

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0296909

DOI: 10.1371/journal.pone.0296909

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