Fourth-order time-stepping compact finite difference method for multi-dimensional space-fractional coupled nonlinear Schrödinger equations

• Published in: SN partial differential equations and applications 2020-12, Vol.1 (6), Article 45
• Main Authors: Almushaira, Mustafa, Liu, Fei
• Format: Article
• Language: English
• Subjects: 2. Computational Approaches; Analysis; Mathematical and Computational Biology; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Original Paper; Partial Differential Equations; Theoretical
• ISSN: 2662-2963; 2662-2971
• DOI: 10.1007/s42985-020-00048-6

In this work, an efficient fourth-order time-stepping compact finite difference scheme is devised for the numerical solution of multi-dimensional space-fractional coupled nonlinear Schrödinger equations. Some existing numerical schemes for these equations lead to full and dense matrices due to the non-locality of the fractional operator. To overcome this challenge, the spatial discretization in our method is carried out by using the compact finite difference scheme and matrix transfer technique in which FFT-based computations can be utilized. This avoids storing the large matrix from discretizing the fractional operator and also significantly reduces the computational costs. The amplification symbol of this scheme is investigated by plotting its stability regions, which indicates the stability of the scheme. Numerical experiments show that this scheme preserves the conservation laws of mass and energy, and achieves the fourth-order accuracy in both space and time.